The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform
Bram Van Putten - One of the best experts on this subject based on the ideXlab platform.
-
Estimation method of multivariate exponential probabilities based on a simple coordinates transform
Journal of Statistical Computation and Simulation, 2010Co-Authors: Niels J. Olieman, Bram Van PuttenAbstract:A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a Measurable Set is introduced and is called the exponential simplex (ES) estimator. For any Measurable Set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped Measurable Sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex Sets, such as convex Sets, the ES estimator can be expressed in a simple analytical form.
-
Estimation method of multivariate exponential probabilities based on a simplex coordinates transform
2006Co-Authors: Niels J. Olieman, Bram Van PuttenAbstract:A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a Measurable Set is introduced and is called the Exponential Simplex (ES) estimator. For any Measurable Set, the standard error of the ES-estimator is at most the standard error of the well known Monte Carlo (MC) estimator. For non-radially shaped Measurable Sets, the ES-estimator has a strictly smaller standard error than the MC-estimator. For ray-convex Sets, such as convex Sets, the ES-estimator can be expressed in a simple analytical form.
James Ledoux - One of the best experts on this subject based on the ideXlab platform.
-
Limit theorems for stationary Markov processes with L2-spectral gap
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2012Co-Authors: Déborah Ferré, Loïc Hervé, James LedouxAbstract:Let $(X_t, Y_t)_{t\in \mathbb{T}}$ be a discrete or continuous-time Markov process with state space $\mathbb{X} \times \mathbb{R}^d$ where $\mathbb{X}$ is an arbitrary Measurable Set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\in \mathbb{T}}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\in \mathbb{T}}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\in \mathbb{T}}$ is shown to satisfy the following classical limit theorems: (a) the central limit theorem, (b) the local limit theorem, (c) the one-dimensional Berry-Esseen theorem, (d) the one-dimensional first-order Edgeworth expansion, provided that we have $\sup\{ t\in(0,1]\cap \mathbb{T} : \mathbb{E}{\pi,0}[|Y_t| ^{\alpha}] 0$ for (c) and (d)). For the statements (b) and (d), a Markov nonlattice condition is also assumed as in the independent case. All the results are derived under the assumption that the Markov process $(X_t)_{t\in \mathbb{T}}$ has an invariant probability distribution $\pi$, is stationary and has the $\mathbb{L}^2(\pi)$-spectral gap property (that is, $(X_t)_{t\in \mathbb{N}}$ is $\rho$-mixing in the discrete-time case). The case where $(X_t)_{t\in \mathbb{T}}$ is non-stationary is briefly discussed. As an application, we derive a Berry-Esseen bound for the M-estimators associated with $\rho$-mixing Markov chains.
-
Limit theorems for stationary Markov processes with L2-spectral gap
Annales de l'IHP - Probabilités et Statistiques, 2012Co-Authors: Déborah Ferré, Loïc Hervé, James LedouxAbstract:Let $(X_t, Y_t)_{t\in \mathbb{T}}$ be a discrete or continuous-time Markov process with state space $\mathbb{X} \times \mathbb{R}^d$ where $\mathbb{X}$ is an arbitrary Measurable Set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\in \mathbb{T}}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\in \mathbb{T}}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\in \mathbb{T}}$ is shown to satisfy the following classical limit theorems: (a) the central limit theorem, (b) the local limit theorem, (c) the one-dimensional Berry-Esseen theorem, (d) the one-dimensional first-order Edgeworth expansion, provided that we have $\sup\{ t\in(0,1]\cap \mathbb{T} : \mathbb{E}{\pi,0}[|Y_t| ^{\alpha}] < 1\}$ with the expected order with respect to the independent case (up to some $\varepsilon > 0$ for (c) and (d)). For the statements (b) and (d), a Markov nonlattice condition is also assumed as in the independent case. All the results are derived under the assumption that the Markov process $(X_t)_{t\in \mathbb{T}}$ has an invariant probability distribution $\pi$, is stationary and has the $\mathbb{L}^2(\pi)$-spectral gap property (that is, $(X_t)_{t\in \mathbb{N}}$ is $\rho$-mixing in the discrete-time case). The case where $(X_t)_{t\in \mathbb{T}}$ is non-stationary is briefly discussed. As an application, we derive a Berry-Esseen bound for the M-estimators associated with $\rho$-mixing Markov chains.
Niels J. Olieman - One of the best experts on this subject based on the ideXlab platform.
-
Estimation method of multivariate exponential probabilities based on a simple coordinates transform
Journal of Statistical Computation and Simulation, 2010Co-Authors: Niels J. Olieman, Bram Van PuttenAbstract:A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a Measurable Set is introduced and is called the exponential simplex (ES) estimator. For any Measurable Set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped Measurable Sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex Sets, such as convex Sets, the ES estimator can be expressed in a simple analytical form.
-
Estimation method of multivariate exponential probabilities based on a simplex coordinates transform
2006Co-Authors: Niels J. Olieman, Bram Van PuttenAbstract:A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a Measurable Set is introduced and is called the Exponential Simplex (ES) estimator. For any Measurable Set, the standard error of the ES-estimator is at most the standard error of the well known Monte Carlo (MC) estimator. For non-radially shaped Measurable Sets, the ES-estimator has a strictly smaller standard error than the MC-estimator. For ray-convex Sets, such as convex Sets, the ES-estimator can be expressed in a simple analytical form.
Yongli Wang - One of the best experts on this subject based on the ideXlab platform.
-
H∞ Control of Discrete-Time Stochastic Systems With Borel-Measurable Markov Jumps
IEEE Access, 2020Co-Authors: Yongli WangAbstract:This paper is concerned with a kind of discrete-time stochastic systems with Markov jump parameters taking values in a Borel Measurable Set. First, both strong exponential stability and exponential stability in the mean square sense are introduced for the considered systems. Based on generalized Lyapunov equation and inequality, necessary and sufficient conditions are derived for the strong exponential stability. By use of the given stability criteria, it is shown that strong exponential stability can lead to exponential stability and further to stochastic stability. Moreover, strong exponential stability can guarantee the so-called l2 input-state stability, which characterizes the asymptotic behavior of system state influenced by exogenous disturbance with finite energy. Second, H performance is analyzed for the perturbed dynamic models over finite and infinite horizons, respectively. For a prescribed disturbance attenuation level, stochastic bound real lemmas are presented in terms of Riccati equations or linear matrix inequalities. As a direct application, the infinite-horizon H∞ control problem is Settled and the state-feedback controller is constructed. Numerical simulations are conducted to illustrate the validity of the proposed results.
Déborah Ferré - One of the best experts on this subject based on the ideXlab platform.
-
Limit theorems for stationary Markov processes with L2-spectral gap
Annales De L Institut Henri Poincare-probabilites Et Statistiques, 2012Co-Authors: Déborah Ferré, Loïc Hervé, James LedouxAbstract:Let $(X_t, Y_t)_{t\in \mathbb{T}}$ be a discrete or continuous-time Markov process with state space $\mathbb{X} \times \mathbb{R}^d$ where $\mathbb{X}$ is an arbitrary Measurable Set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\in \mathbb{T}}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\in \mathbb{T}}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\in \mathbb{T}}$ is shown to satisfy the following classical limit theorems: (a) the central limit theorem, (b) the local limit theorem, (c) the one-dimensional Berry-Esseen theorem, (d) the one-dimensional first-order Edgeworth expansion, provided that we have $\sup\{ t\in(0,1]\cap \mathbb{T} : \mathbb{E}{\pi,0}[|Y_t| ^{\alpha}] 0$ for (c) and (d)). For the statements (b) and (d), a Markov nonlattice condition is also assumed as in the independent case. All the results are derived under the assumption that the Markov process $(X_t)_{t\in \mathbb{T}}$ has an invariant probability distribution $\pi$, is stationary and has the $\mathbb{L}^2(\pi)$-spectral gap property (that is, $(X_t)_{t\in \mathbb{N}}$ is $\rho$-mixing in the discrete-time case). The case where $(X_t)_{t\in \mathbb{T}}$ is non-stationary is briefly discussed. As an application, we derive a Berry-Esseen bound for the M-estimators associated with $\rho$-mixing Markov chains.
-
Limit theorems for stationary Markov processes with L2-spectral gap
Annales de l'IHP - Probabilités et Statistiques, 2012Co-Authors: Déborah Ferré, Loïc Hervé, James LedouxAbstract:Let $(X_t, Y_t)_{t\in \mathbb{T}}$ be a discrete or continuous-time Markov process with state space $\mathbb{X} \times \mathbb{R}^d$ where $\mathbb{X}$ is an arbitrary Measurable Set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\in \mathbb{T}}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\in \mathbb{T}}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\in \mathbb{T}}$ is shown to satisfy the following classical limit theorems: (a) the central limit theorem, (b) the local limit theorem, (c) the one-dimensional Berry-Esseen theorem, (d) the one-dimensional first-order Edgeworth expansion, provided that we have $\sup\{ t\in(0,1]\cap \mathbb{T} : \mathbb{E}{\pi,0}[|Y_t| ^{\alpha}] < 1\}$ with the expected order with respect to the independent case (up to some $\varepsilon > 0$ for (c) and (d)). For the statements (b) and (d), a Markov nonlattice condition is also assumed as in the independent case. All the results are derived under the assumption that the Markov process $(X_t)_{t\in \mathbb{T}}$ has an invariant probability distribution $\pi$, is stationary and has the $\mathbb{L}^2(\pi)$-spectral gap property (that is, $(X_t)_{t\in \mathbb{N}}$ is $\rho$-mixing in the discrete-time case). The case where $(X_t)_{t\in \mathbb{T}}$ is non-stationary is briefly discussed. As an application, we derive a Berry-Esseen bound for the M-estimators associated with $\rho$-mixing Markov chains.