Constant step stochastic approximations involving differential inclusions: stability, long-run convergence and applications

@article{Bianchi2016ConstantSS,
  title={Constant step stochastic approximations involving differential inclusions: stability, long-run convergence and applications},
  author={P. Bianchi and W. Hachem and A. Salim},
  journal={Stochastics},
  year={2016},
  volume={91},
  pages={288 - 320}
}
ABSTRACT We consider a Markov chain whose kernel is indexed by a scaling parameter , referred to as the step size. The aim is to analyze the behaviour of the Markov chain in the doubly asymptotic regime where then . First, under mild assumptions on the so-called drift of the Markov chain, we show that the interpolated process converges narrowly to the solutions of a Differential Inclusion (DI) involving an upper semicontinuous set-valued map with closed and convex values. Second, we provide… Expand
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References

SHOWING 1-10 OF 43 REFERENCES
Stochastic Approximations with Constant Step Size and Differential Inclusions
  • 50
  • PDF
Stochastic recursive inclusions with non-additive iterate-dependent Markov noise
  • 6
  • PDF
Markov chains with discontinuous drifts have differential inclusion limits
  • 39
  • PDF
Dynamical Behavior of a Stochastic Forward–Backward Algorithm Using Random Monotone Operators
  • 20
  • PDF
Stochastic Approximations and Differential Inclusions, Part II: Applications
  • 94
  • PDF
Asymptotic Behavior of a Markovian Stochastic Algorithm with Constant Step
  • 30
Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition
  • 424
  • PDF
Ergodic Properties of Weak Asymptotic Pseudotrajectories for Semiflows
  • 16
  • PDF
Stochastic Approximations and Differential Inclusions
  • 233
  • PDF
Ergodic Properties of weak Asymptotic Pseudotrajectories for Set-valued Dynamical Systems
  • 4
  • Highly Influential
  • PDF
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