The Experts below are selected from a list of 1554 Experts worldwide ranked by ideXlab platform
Lauri Viitasaari - One of the best experts on this subject based on the ideXlab platform.
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representation of Stationary and Stationary Increment processes via langevin equation and self similar processes
Statistics & Probability Letters, 2016Co-Authors: Lauri ViitasaariAbstract:Let Wt be a standard Brownian motion. It is well-known that the Langevin equation dUt=−θUtdt+dWt defines a Stationary process called Ornstein–Uhlenbeck process. Furthermore, Langevin equation can be used to construct other Stationary processes by replacing Brownian motion Wt with some other process G with Stationary Increments. In this article we prove that the converse also holds and all continuous Stationary processes arise from a Langevin equation with certain noise G=Gθ. Discrete analogies of our results are given and applications are discussed.
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representation of Stationary and Stationary Increment processes via langevin equation and self similar processes
arXiv: Probability, 2014Co-Authors: Lauri ViitasaariAbstract:Let $W_t$ be a standard Brownian motion. It is well-known that the Langevin equation $d U_t = -\theta U_td t + d W_t$ defines a Stationary process called Ornstein-Uhlenbeck process. Furthermore, Langevin equation can be used to construct other Stationary processes by replacing Brownian motion $W_t$ with some other process $G$ with Stationary Increments. In this article we prove that the converse also holds and all continuous Stationary processes arise from a Langevin equation with certain noise $G=G_\theta$. Discrete analogies of our results are given and applications are discussed.
Gustavo Didier - One of the best experts on this subject based on the ideXlab platform.
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the asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments
Journal of Time Series Analysis, 2017Co-Authors: Gustavo Didier, Kui ZhangAbstract:Microrheology is the study of the properties of biological complex fluids through the anomalous diffusion of small embedded particles. The main statistic for characterizing anomalous diffusion is the so-named mean squared displacement (MSD) of the particles. Notwithstanding the central statistical role of the MSD, its asymptotic distribution has not yet been established. In this paper, we assume that the particle motion is a Gaussian, Stationary-Increment stochastic process. We show that as the sample and the Increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusion exponent parameter.
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the asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments
arXiv: Probability, 2015Co-Authors: Gustavo Didier, Kui ZhangAbstract:Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the properties of complex fluids, such as those found in biology, through the dynamics of small embedded particles, typically latex beads. Statistics based on the recorded sample paths are then used by biophysicists to infer rheological properties of the fluid. In the biophysical literature, the main statistic for characterizing diffusivity is the so-named mean square displacement (MSD) of the tracer particles. Notwithstanding the central role played by the MSD, its asymptotic distribution in different cases has not yet been established. In this paper, we tackle this problem. We take a pathwise approach and assume that the particle movement undergoes a Gaussian, Stationary-Increment stochastic process. We show that as the sample and the Increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusivity parameter. We illustrate our results analytically and computationally based on fractional Brownian motion and the (integrated) fractional Ornstein-Uhlenbeck process.
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on integral representations of operator fractional brownian fields
Statistics & Probability Letters, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Abstract Operator fractional Brownian fields (OFBFs) are Gaussian, Stationary-Increment vector random fields that satisfy the operator self-similarity relation { X ( c E t ) } t ∈ R m = L { c H X ( t ) } t ∈ R m . We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be re-expressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al. (2007).
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on integral representations of operator fractional brownian fields
arXiv: Probability, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian fields (OFBFs) are Gaussian, Stationary-Increment vector random fields that satisfy the operator self-similarity relation {X(c^{E}t)}_{t in R^m} L= {c^{H}X(t)}_{t in R^m}. We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be reexpressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al.(2007), "Operator scaling stable random fields", Stochastic Processes and their Applications 117, 312--332.
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integral representations and properties of operator fractional brownian motions
arXiv: Statistics Theory, 2011Co-Authors: Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) Stationary Increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time-reversibility, the defining properties (i)--(iii) do not, in general, characterize the covariance structure of OFBMs. To circumvent this problem, the class of OFBMs is characterized here by means of their integral representations in the spectral and time domains. For the spectral domain representations, this involves showing how the operator self-similarity shapes the spectral density in the general representation of Stationary Increment processes. The time domain representations are derived by using primary matrix functions and taking the Fourier transforms of the deterministic spectral domain kernels. Necessary and sufficient conditions for OFBMs to be time-reversible are established in terms of their spectral and time domain representations. It is also shown that the spectral density of the Stationary Increments of an OFBM has a rigid structure, here called the dichotomy principle. The notion of operator Brownian motions is also explored.
Vladas Pipiras - One of the best experts on this subject based on the ideXlab platform.
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on integral representations of operator fractional brownian fields
Statistics & Probability Letters, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Abstract Operator fractional Brownian fields (OFBFs) are Gaussian, Stationary-Increment vector random fields that satisfy the operator self-similarity relation { X ( c E t ) } t ∈ R m = L { c H X ( t ) } t ∈ R m . We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be re-expressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al. (2007).
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on integral representations of operator fractional brownian fields
arXiv: Probability, 2014Co-Authors: Changryong Baek, Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian fields (OFBFs) are Gaussian, Stationary-Increment vector random fields that satisfy the operator self-similarity relation {X(c^{E}t)}_{t in R^m} L= {c^{H}X(t)}_{t in R^m}. We establish a general harmonizable representation (Fourier domain stochastic integral) for OFBFs. Under additional assumptions, we also show how the harmonizable representation can be reexpressed as a moving average stochastic integral, thus answering an open problem described in Bierme et al.(2007), "Operator scaling stable random fields", Stochastic Processes and their Applications 117, 312--332.
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integral representations and properties of operator fractional brownian motions
arXiv: Statistics Theory, 2011Co-Authors: Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) Stationary Increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time-reversibility, the defining properties (i)--(iii) do not, in general, characterize the covariance structure of OFBMs. To circumvent this problem, the class of OFBMs is characterized here by means of their integral representations in the spectral and time domains. For the spectral domain representations, this involves showing how the operator self-similarity shapes the spectral density in the general representation of Stationary Increment processes. The time domain representations are derived by using primary matrix functions and taking the Fourier transforms of the deterministic spectral domain kernels. Necessary and sufficient conditions for OFBMs to be time-reversible are established in terms of their spectral and time domain representations. It is also shown that the spectral density of the Stationary Increments of an OFBM has a rigid structure, here called the dichotomy principle. The notion of operator Brownian motions is also explored.
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integral representations and properties of operator fractional brownian motions
Bernoulli, 2011Co-Authors: Gustavo Didier, Vladas PipirasAbstract:Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar, and (iii) Stationary Increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time reversibility, the deflning properties (i)-(iii) do not, in general, characterize the covariance structure of OFBMs. To circumvent this problem, the class of OFBMs is characterized here through their integral representations in the spectral and time domains. For the spectral domain representations, this involves showing how the operator self-similarity shapes the spectral density in the general representation of Stationary Increment processes. The time domain representations are derived by using primary matrix functions and by taking the Fourier transform of the deterministic spectral domain kernels. Necessary and su‐cient conditions for OFBMs to be time reversible are established in terms of their spectral and time domain representations. It is also shown that the spectral density of the Stationary Increments of OFBM has a rigid structure, called here Dichotomy Principle. The notion of operator Brownian motions is also explored.
Kui Zhang - One of the best experts on this subject based on the ideXlab platform.
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the asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments
Journal of Time Series Analysis, 2017Co-Authors: Gustavo Didier, Kui ZhangAbstract:Microrheology is the study of the properties of biological complex fluids through the anomalous diffusion of small embedded particles. The main statistic for characterizing anomalous diffusion is the so-named mean squared displacement (MSD) of the particles. Notwithstanding the central statistical role of the MSD, its asymptotic distribution has not yet been established. In this paper, we assume that the particle motion is a Gaussian, Stationary-Increment stochastic process. We show that as the sample and the Increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusion exponent parameter.
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the asymptotic distribution of the pathwise mean squared displacement in single particle tracking experiments
arXiv: Probability, 2015Co-Authors: Gustavo Didier, Kui ZhangAbstract:Recent advances in light microscopy have spawned new research frontiers in microbiology by working around the diffraction barrier and allowing for the observation of nanometric biological structures. Microrheology is the study of the properties of complex fluids, such as those found in biology, through the dynamics of small embedded particles, typically latex beads. Statistics based on the recorded sample paths are then used by biophysicists to infer rheological properties of the fluid. In the biophysical literature, the main statistic for characterizing diffusivity is the so-named mean square displacement (MSD) of the tracer particles. Notwithstanding the central role played by the MSD, its asymptotic distribution in different cases has not yet been established. In this paper, we tackle this problem. We take a pathwise approach and assume that the particle movement undergoes a Gaussian, Stationary-Increment stochastic process. We show that as the sample and the Increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusivity parameter. We illustrate our results analytically and computationally based on fractional Brownian motion and the (integrated) fractional Ornstein-Uhlenbeck process.
Guangjun Liu - One of the best experts on this subject based on the ideXlab platform.
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active model based predictive control and experimental investigation on unmanned helicopters in full flight envelope
IEEE Transactions on Control Systems and Technology, 2013Co-Authors: Dalei Song, Jianda Han, Guangjun LiuAbstract:For the control of unmanned helicopters in full flight envelope, an active model based predictive control scheme is developed in this brief. Dynamics in full envelope is modeled, with uncertainties represented by the system model error and process noise. The model error depends on both helicopter dynamics and flight mode, and the process noise is assumed unknown but bounded. Based on the set-membership filter, an active modeling based Stationary Increment predictive control, based on the estimated model error and its boundary to optimally compensate the model error, as well as the aerodynamics time delay, is proposed. The proposed method has been implemented on the ServoHeli-40 unmanned helicopter platform and experimentally tested; the results have demonstrated its effectiveness.
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active model based predictive control for unmanned helicopter in full flight envelope
Intelligent Robots and Systems, 2010Co-Authors: Dalei Song, Jianda Han, Guangjun LiuAbstract:For the control of unmanned helicopters in full flight envelope, an active model based control scheme is developed in this paper. An adaptive set-membership filter (ASMF) is used to online estimate both the model error due to flight mode change and its boundary, taking advantage of ASMF, so that the model error can be assumed unknown but bounded (UBB). The proposed approach is practical because the model error depends on both helicopter dynamics and flight states, and may not be assumed as white noise. An active modeling based Stationary Increment predictive control (AMSIPC) is also proposed based on the estimated model error and its boundary to optimally compensate the model error, as well as the aerodynamics time delay. The proposed method has been implemented on the ServoHeli-20 unmanned helicopter platform and experimentally tested, and the results have demonstrated its effectiveness.