Borkar, Vivek ; Gaitsgory, Vladimir (2005) On existence of limit occupational measures set of a controlled stochastic differential equation SIAM Journal on Control and Optimization, 44 (4). pp. 1436-1473. ISSN 0363-0129
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Official URL: http://epubs.siam.org/sicon/resource/1/sjcodc/v44/...
Related URL: http://dx.doi.org/10.1137/S0363012904443476
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Society for Industrial and Applied Mathematics. |
| Keywords: | Singularly Perturbed Controlled Stochastic Differential Equations; Occupational Measures; Averaging Method; Limit Occupational Measures Sets; Approximation Of Slow Motions |
| ID Code: | 81463 |
| Deposited On: | 07 Feb 2012 04:54 |
| Last Modified: | 07 Feb 2012 04:54 |
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