The Experts below are selected from a list of 8484 Experts worldwide ranked by ideXlab platform

Oleksandr Kutoviy - One of the best experts on this subject based on the ideXlab platform.

  • the statistical dynamics of a spatial logistic model and the related kinetic equation
    Mathematical Models and Methods in Applied Sciences, 2015
    Co-Authors: Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky, Oleksandr Kutoviy
    Abstract:

    In this paper, we study an infinite system of point entities in ℝd which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is described by means of a BBGKY-type equation for the corresponding correlation (moment) functions. It is proved that: (a) these functions evolve on a Bounded Time Interval and remain sub-Poissonian due to the competition; (b) in the Vlasov scaling limit they converge to the correlation functions of the Time-dependent Poisson point field the density of which solves the kinetic equation obtained in the scaling limit from the equation for the correlation functions. A number of properties of the solutions of the kinetic equation are also esta- blished.

  • the statistical dynamics of a spatial logistic model and the related kinetic equation
    arXiv: Mathematical Physics, 2014
    Co-Authors: Dmitri Finkelshtein, Yuri Kondratiev, Yuri Kozitsky, Oleksandr Kutoviy
    Abstract:

    There is studied an infinite system of point entities in $\mathbb{R}^d$ which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is described by means of a BBGKY-type equation for the corresponding correlation (moment) functions. It is proved that: (a) these functions evolve on a Bounded Time Interval and remain sub-Poissonian due to the competition; (b) in the Vlasov scaling limit they converge to the correlation functions of the Time-dependent Poisson point field the density of which solves the kinetic equation obtained in the scaling limit from the equation for the correlation functions. A number of properties of the solutions of the kinetic equation are also established.

Michael Ostrovsky - One of the best experts on this subject based on the ideXlab platform.

  • information aggregation in dynamic markets with strategic traders
    Econometrica, 2012
    Co-Authors: Michael Ostrovsky
    Abstract:

    This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that, for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a Bounded Time Interval, and in every equilibrium, as Time approaches the end of the Interval, the market price of a “separable” security converges in probability to its expected value conditional on the traders' pooled information. If the security is “non-separable,” then there exists a common prior over the states of the world and an equilibrium such that information does not get aggregated. The class of separable securities includes, among others, Arrow–Debreu securities, whose value is 1 in one state of the world and 0 in all others, and “additive” securities, whose value can be interpreted as the sum of traders' signals.

  • information aggregation in dynamic markets with strategic traders
    Electronic Commerce, 2009
    Co-Authors: Michael Ostrovsky
    Abstract:

    This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a Bounded Time Interval, and in every equilibrium, as Time approaches the end of the Interval, the market price of a "separable" security converges in probability to its expected value based on the traders' pooled information.

  • information aggregation in dynamic markets with strategic traders
    Research Papers in Economics, 2009
    Co-Authors: Michael Ostrovsky
    Abstract:

    This paper studies information aggregation in dynamic markets with a finite number of partially informed strategic traders. It shows that for a broad class of securities, information in such markets always gets aggregated. Trading takes place in a Bounded Time Interval, and in every equilibrium, as Time approaches the end of the Interval, the market price of a "separable" security converges in probability to its expected value conditional on the traders' pooled information. If the security is "non-separable," then there exists a common prior over the states of the world and an equilibrium such that information does not get aggregated. The class of separable securities includes, among others, Arrow-Debreu securities, whose value is one in one state of the world and zero in all others, and "additive" securities, whose value can be interpreted as the sum of traders' signals.

Igor G Vladimirov - One of the best experts on this subject based on the ideXlab platform.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    Applied Mathematics and Optimization, 2021
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. Such functionals are related to more conservative behaviour and robustness of systems with respect to statistical uncertainty, which makes the challenging problems of their computation and minimization practically important. To this end, we obtain an integro-differential equation for the Time evolution of the quadratic–exponential functional, which is different from the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. Further approximations of the cost functional, based on higher-order cumulants and their growth rates, are applied to large deviations estimates in the form of upper bounds for tail distributions. We discuss an auxiliary classical Gaussian–Markov diffusion process in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different fourth-order cumulants, thus showing that the risk-sensitive criteria are not reducible to quadratic–exponential moments of classical Gaussian processes. The results of the paper are illustrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    IFAC-PapersOnLine, 2020
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    Abstract This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    arXiv: Quantum Physics, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its asymptotic infinite-horizon growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formulas express the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide two illustrations including a numerical example with a two-mode oscillator.

  • a quantum karhunen loeve expansion and quadratic exponential functionals for linear quantum stochastic systems
    arXiv: Probability, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in the vacuum state is organised as a series of sinusoidal functions on a Bounded Time Interval with statistically independent coefficients consisting of noncommuting position and momentum operators in a Gaussian quantum state. A similar representation is obtained for the solution of a linear quantum stochastic differential equation which governs the system variables of an open quantum harmonic oscillator. This expansion is applied to computing a quadratic-exponential functional arising as a performance criterion in the framework of risk-sensitive control for this class of open quantum systems.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    arXiv: Optimization and Control, 2017
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. An integro-differential equation is obtained for the Time evolution of this quadratic-exponential functional, which is compared with the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. We also outline further approximations of the cost functional, based on higher-order cumulants and their growth rates, together with large deviations estimates. For comparison, an auxiliary classical Gaussian Markov diffusion process is considered in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different higher-order moments relevant to the risk-sensitive criteria. The results of the paper are also demonstrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

Matthew R James - One of the best experts on this subject based on the ideXlab platform.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    Applied Mathematics and Optimization, 2021
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. Such functionals are related to more conservative behaviour and robustness of systems with respect to statistical uncertainty, which makes the challenging problems of their computation and minimization practically important. To this end, we obtain an integro-differential equation for the Time evolution of the quadratic–exponential functional, which is different from the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. Further approximations of the cost functional, based on higher-order cumulants and their growth rates, are applied to large deviations estimates in the form of upper bounds for tail distributions. We discuss an auxiliary classical Gaussian–Markov diffusion process in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different fourth-order cumulants, thus showing that the risk-sensitive criteria are not reducible to quadratic–exponential moments of classical Gaussian processes. The results of the paper are illustrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    IFAC-PapersOnLine, 2020
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    Abstract This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    arXiv: Quantum Physics, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its asymptotic infinite-horizon growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formulas express the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide two illustrations including a numerical example with a two-mode oscillator.

  • a quantum karhunen loeve expansion and quadratic exponential functionals for linear quantum stochastic systems
    arXiv: Probability, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in the vacuum state is organised as a series of sinusoidal functions on a Bounded Time Interval with statistically independent coefficients consisting of noncommuting position and momentum operators in a Gaussian quantum state. A similar representation is obtained for the solution of a linear quantum stochastic differential equation which governs the system variables of an open quantum harmonic oscillator. This expansion is applied to computing a quadratic-exponential functional arising as a performance criterion in the framework of risk-sensitive control for this class of open quantum systems.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    arXiv: Optimization and Control, 2017
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. An integro-differential equation is obtained for the Time evolution of this quadratic-exponential functional, which is compared with the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. We also outline further approximations of the cost functional, based on higher-order cumulants and their growth rates, together with large deviations estimates. For comparison, an auxiliary classical Gaussian Markov diffusion process is considered in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different higher-order moments relevant to the risk-sensitive criteria. The results of the paper are also demonstrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

Ian R Petersen - One of the best experts on this subject based on the ideXlab platform.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    Applied Mathematics and Optimization, 2021
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. Such functionals are related to more conservative behaviour and robustness of systems with respect to statistical uncertainty, which makes the challenging problems of their computation and minimization practically important. To this end, we obtain an integro-differential equation for the Time evolution of the quadratic–exponential functional, which is different from the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. Further approximations of the cost functional, based on higher-order cumulants and their growth rates, are applied to large deviations estimates in the form of upper bounds for tail distributions. We discuss an auxiliary classical Gaussian–Markov diffusion process in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different fourth-order cumulants, thus showing that the risk-sensitive criteria are not reducible to quadratic–exponential moments of classical Gaussian processes. The results of the paper are illustrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    IFAC-PapersOnLine, 2020
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    Abstract This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its infinite-horizon asymptotic growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formula expresses the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide an illustrative numerical example with a two-mode open quantum harmonic oscillator.

  • frequency domain computation of quadratic exponential cost functionals for linear quantum stochastic systems
    arXiv: Quantum Physics, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with quadratic-exponential functionals (QEFs) as risk-sensitive performance criteria for linear quantum stochastic systems driven by multichannel bosonic fields. Such costs impose an exponential penalty on quadratic functions of the quantum system variables over a Bounded Time Interval, and their minimization secures a number of robustness properties for the system. We use an integral operator representation of the QEF, obtained recently, in order to compute its asymptotic infinite-horizon growth rate in the invariant Gaussian state when the stable system is driven by vacuum input fields. The resulting frequency-domain formulas express the QEF growth rate in terms of two spectral functions associated with the real and imaginary parts of the quantum covariance kernel of the system variables. We also discuss the computation of the QEF growth rate using homotopy and contour integration techniques and provide two illustrations including a numerical example with a two-mode oscillator.

  • a quantum karhunen loeve expansion and quadratic exponential functionals for linear quantum stochastic systems
    arXiv: Probability, 2019
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in the vacuum state is organised as a series of sinusoidal functions on a Bounded Time Interval with statistically independent coefficients consisting of noncommuting position and momentum operators in a Gaussian quantum state. A similar representation is obtained for the solution of a linear quantum stochastic differential equation which governs the system variables of an open quantum harmonic oscillator. This expansion is applied to computing a quadratic-exponential functional arising as a performance criterion in the framework of risk-sensitive control for this class of open quantum systems.

  • multi point gaussian states quadratic exponential cost functionals and large deviations estimates for linear quantum stochastic systems
    arXiv: Optimization and Control, 2017
    Co-Authors: Igor G Vladimirov, Ian R Petersen, Matthew R James
    Abstract:

    This paper is concerned with risk-sensitive performance analysis for linear quantum stochastic systems interacting with external bosonic fields. We consider a cost functional in the form of the exponential moment of the integral of a quadratic polynomial of the system variables over a Bounded Time Interval. An integro-differential equation is obtained for the Time evolution of this quadratic-exponential functional, which is compared with the original quantum risk-sensitive performance criterion employed previously for measurement-based quantum control and filtering problems. Using multi-point Gaussian quantum states for the past history of the system variables and their first four moments, we discuss a quartic approximation of the cost functional and its infinite-horizon asymptotic behaviour. The computation of the asymptotic growth rate of this approximation is reduced to solving two algebraic Lyapunov equations. We also outline further approximations of the cost functional, based on higher-order cumulants and their growth rates, together with large deviations estimates. For comparison, an auxiliary classical Gaussian Markov diffusion process is considered in a complex Euclidean space which reproduces the quantum system variables at the level of covariances but has different higher-order moments relevant to the risk-sensitive criteria. The results of the paper are also demonstrated by a numerical example and may find applications to coherent quantum risk-sensitive control problems, where the plant and controller form a fully quantum closed-loop system, and other settings with nonquadratic cost functionals.