The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Clément Dombry - One of the best experts on this subject based on the ideXlab platform.
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Discrete Approximation of stable white noise - Application to spatial linear filtering
arXiv: Probability, 2009Co-Authors: Clément DombryAbstract:Motivated by the simulation of stable random fields, we consider the issue of Discrete Approximations of independently scattered stable noise. Two approaches are proposed: grid Approximations available when the underlying space is $\bbR^d$ and shot noise Approximations available on more general spaces. Limit theorems stating the convergence of Discrete random noises to stable white noise are proved. These results are then applied to study moving average spatial random fields with heavy-tailed innovations and related limit theorems. A second application deals with Discrete Approximation for Brownian L\'evy motion on the sphere or on the euclidean space.
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Discrete Approximation of a stable self-similar stationary increments process
Bernoulli, 2009Co-Authors: Clément Dombry, Nadine Guillotin-plantardAbstract:The aim of this paper is to present a result of Discrete Approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and con vergence theorems are available only in the case of stable L?vy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema first introduced by Cohen and Samorodnitsky, which we consider in a more general setting. Strong relationships with Kesten and Spitzer's random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.
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Discrete Approximation of a stable self-similar stationary increments process
arXiv: Probability, 2008Co-Authors: Clément Dombry, Nadine Guillotin-plantardAbstract:The aim of this paper is to present a result of Discrete Approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context in which such processes can arise. To our knowledge, discretisation and convergence theorems are available only in the case of stable L\'evy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema, which was firstly introduced by Cohen and Samorodnitsky, and that we consider in a more general setting. Strong relationships with Kesten and Spitzer's random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.
Takuro Kida - One of the best experts on this subject based on the ideXlab platform.
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Theory of the optimum Discrete running Approximation of multi-dimensional approximately band-limited signals
2009 16th International Conference on Digital Signal Processing, 2009Co-Authors: Yuichi Kida, Takuro KidaAbstract:In this paper, we present an n-dimensional running Discrete Approximation that minimizes various worst-case measures of error, simultaneously. We derive continuous space-limited n-dimensional interpolation-functions satisfying condition that is called Discrete orthogonality. Then, we present a set of signals that satisfies two conditions of the optimum Approximation.
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The FIR filter bank with given analysis filters that minimizes various worst-case measures of error at the same time
2005 IEEE International Symposium on Circuits and Systems, 2005Co-Authors: Yuichi Kida, Takuro KidaAbstract:We present a scan-type Discrete Approximation of an FIR filter bank that minimizes various worst-case measures of error, including the long-range worst-case measures of error in the time-domain or the frequency-domain. Discrete interpolation functions are presented which vanish outside the prescribed domain in the integer time-axis and are realized by FIR filters.
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Optimum Discrete Approximation of multidimensional band-limited signals
Multimedia Systems and Applications VI, 2003Co-Authors: Yuichi Kida, Takuro KidaAbstract:We present a necessary and sufficient condition that a given n-dimensional generalized interpolation Approximation minimizes various worst-case measures of error of Approximation at the same time among all the Approximations, including nonlinear Approximation, using the same set of sample values. As a typical example of the optimum Approximation satisfying the above necessary and sufficient condition, we present n-dimensional generalitd interpolation Approximation using the finite number of sample values. Then, we consider n-dimensional generalized Discrete interpolation Approximation based on n-dimensional FIR filter banks that uses the finite number of sample values in the Approximation of each pixel of image but scan the image over the whole pixels. For this scanning-type Discrete Approximation, we prove that Discrete interpolation functions exist that minimize various measures of error of Approximation defined at Discrete sample points x p =p , simultaneously, where p are the n-dimensional integer vectors. The presented Discrete interpolation functions vanish outside the prescribed domain in the integer-vector space. Hence, these interpolation functions are realized by n-dimensional FIR filters. In this discussion, we prove that there exist continuous interpolation functions with extended band-width that interpolate the above Discrete interpolation functions and satisfy the condition called Discrete orthogonality. This condition is one of the two conditions that constitute the necessary and sufficient condition presented in this paper. Several Discrete Approximations are presented that satisfy both the conditions constituting the necessary and sufficient condition presented in this paper. The above Discrete interpolation functions have much flexibility in their frequency characteristics if appropriate analysis filters are selected.
Nadine Guillotin-plantard - One of the best experts on this subject based on the ideXlab platform.
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Discrete Approximation of a stable self-similar stationary increments process
Bernoulli, 2009Co-Authors: Clément Dombry, Nadine Guillotin-plantardAbstract:The aim of this paper is to present a result of Discrete Approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and con vergence theorems are available only in the case of stable L?vy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema first introduced by Cohen and Samorodnitsky, which we consider in a more general setting. Strong relationships with Kesten and Spitzer's random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.
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Discrete Approximation of a stable self-similar stationary increments process
arXiv: Probability, 2008Co-Authors: Clément Dombry, Nadine Guillotin-plantardAbstract:The aim of this paper is to present a result of Discrete Approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context in which such processes can arise. To our knowledge, discretisation and convergence theorems are available only in the case of stable L\'evy motions and fractional Brownian motions. This paper yields new results in this direction. Our main result is the convergence of the random rewards schema, which was firstly introduced by Cohen and Samorodnitsky, and that we consider in a more general setting. Strong relationships with Kesten and Spitzer's random walk in random sceneries are evidenced. Finally, we study some path properties of the limit process.
Timo Welti - One of the best experts on this subject based on the ideXlab platform.
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strong convergence for explicit space time Discrete numerical Approximation methods for stochastic burgers equations
Journal of Mathematical Analysis and Applications, 2019Co-Authors: Arnulf Jentzen, Diyora Salimova, Timo WeltiAbstract:Abstract In this paper we propose and analyze explicit space–time Discrete numerical Approximations for additive space–time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic Burgers equation with space–time white noise. The main result of this paper proves that the proposed explicit space–time Discrete Approximation method converges strongly to the solution process of the stochastic Burgers equation with space–time white noise. To the best of our knowledge, the main result of this work is the first result in the literature which establishes strong convergence for a space–time Discrete Approximation method in the case of the stochastic Burgers equations with space–time white noise.
Alexander M Davie - One of the best experts on this subject based on the ideXlab platform.
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differential equations driven by rough paths an approach via Discrete Approximation
Applied Mathematics Research Express, 2010Co-Authors: Alexander M DavieAbstract:driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler Approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.
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differential equations driven by rough paths an approach via Discrete Approximation
arXiv: Probability, 2007Co-Authors: Alexander M DavieAbstract:A theory of differential equations driven by a non-differentiable path has recently been developed by Lyons. We develop an alternative approach to this theory, using (modified Euler Approximations), and investigate its applicability to stochastic differential equations driven by Brownian motion. We also give some other examples showing that the main results are reasonably sharp.