On existence of limit occupational measures set of a controlled stochastic differential equation
Date
2005
Authors
Borkar, V.
Gaitsgory, V.
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SIAM Journal of Control and Optimization, 2005; 44(4):1436-1473
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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.
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Copyright 2005 Society for Industrial and Applied Mathematics