Existence of limit occupational measures set used for averaging of singularly perturbed controlled stochastic differential equations

Vivek Borkar*, Vladimir Gaitsgory

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

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
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages326-331
Number of pages6
ISBN (Print)1424401712, 9781424401710
Publication statusPublished - 2006
Externally publishedYes
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: 13 Dec 200615 Dec 2006

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period13/12/0615/12/06

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  • Cite this

    Borkar, V., & Gaitsgory, V. (2006). Existence of limit occupational measures set used for averaging of singularly perturbed controlled stochastic differential equations. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 326-331). [4178126] Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE).