On existence of limit occupational measures set of a controlled stochastic differential equation

Vivek Borkar*, Vladimir Gaitsgory

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We establish that, under certain conditions, the set of occupational measures as well as the set of mathematical expectations of occupational measures generated by the admissible controls and the corresponding solutions of a controlled stochastic differential equation (CSDE) converge (with the time horizon tending to infinity) to a set called limit occupational measures set (LOMS) and we show that this limit set coincides with the set of stationary marginal distributions of the CSDE. We also demonstrate the applicability of our results for averaging of singularly perturbed CSDE.

Original languageEnglish
Pages (from-to)1436-1473
Number of pages38
JournalSIAM Journal on Control and Optimization
Volume44
Issue number4
DOIs
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Approximation of slow motions
  • Averaging method
  • Limit occupational measures sets
  • Occupational measures
  • Singularly perturbed controlled stochastic differential equations

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