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

  title={Constant step stochastic approximations involving differential inclusions: stability, long-run convergence and applications},
  author={P. Bianchi and W. Hachem and A. Salim},
  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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