Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques à pas decroissant

DOI10.1007/BF00699098zbMath0588.62153OpenAlexW2090340215MaRDI QIDQ1073522

Michel Métivier, Pierre Priouret

Publication date: 1987

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00699098

zbMATH Keywords

Markov chainpositive recurrenceglobal Lyapunov functionalmost sure convergence theorempathwise asymptotic behaviour of stochastic algorithms

Mathematics Subject Classification ID

Strong limit theorems (60F15) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20) Stochastic approximation (62L20) Sequential estimation (62L12)

Related Items (18)

An adaptive simulated annealing algorithm. ⋮ Vertex-reinforced random walks and a conjecture of Pemantle ⋮ Parametric inference for imperfectly observed Gibbsian fields ⋮ Abstract stochastic approximations and applications ⋮ Stochastic approximation with discontinuous dynamics, differential inclusions, and applications ⋮ Unnamed Item ⋮ Bridging the gap between constant step size stochastic gradient descent and Markov chains ⋮ Dynamics of Morse-Smale urn processes ⋮ Dynamics of vertex-reinforced random walks ⋮ Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach. Part II: Theoretical Analysis ⋮ Stochastic optimization with momentum: convergence, fluctuations, and traps avoidance ⋮ Non asymptotic controls on a recursive superquantile approximation ⋮ Fluctuations of the empirical measure of freezing Markov chains ⋮ Gradient estimates for the performance of Markov chains and discrete event processes ⋮ Stochastic approximation of quasi-stationary distributions for diffusion processes in a bounded domain ⋮ Analysis of an identification algorithm arising in the adaptive estimation of Markov chains ⋮ Revisiting the ODE method for recursive algorithms: fast convergence using quasi stochastic approximation ⋮ A Liapounov bound for solutions of the Poisson equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic approximation with discontinuous dynamics and state dependent noise: w.p. 1 and weak convergence
• Stochastic approximation methods for constrained and unconstrained systems
• Convergence analysis of self-adaptive equalizers
• An Invariant Measure Approach to the Convergence of Stochastic Approximations with State Dependent Noise
• Applications of a Kushner and Clark lemma to general classes of stochastic algorithms
• Analysis of stochastic gradient algorithms for linear regression problems
• Analysis of stochastic approximation schemes with discontinuous and dependent forcing terms with applications to data communication algorithms
• Analysis of recursive stochastic algorithms

This page was built for publication: Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques à pas decroissant