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

Vivek Borkar; Vladimir Gaitsgory

doi:10.1137/S0363012904443476

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 journal › Article › peer-review

17 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 language	English
Pages (from-to)	1436-1473
Number of pages	38
Journal	SIAM Journal on Control and Optimization
Volume	44
Issue number	4
DOIs	https://doi.org/10.1137/S0363012904443476
Publication status	Published - 2005
Externally published	Yes

Keywords

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

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10.1137/S0363012904443476

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AB - 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.

KW - Approximation of slow motions

KW - Averaging method

KW - Limit occupational measures sets

KW - Occupational measures

KW - Singularly perturbed controlled stochastic differential equations

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

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Keywords

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