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

Vivek Borkar; Vladimir Gaitsgory

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

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	326-331
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
Publication status	Published - 2006
Externally published	Yes
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006

Other

Other	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	13/12/06 → 15/12/06

Cite this

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title = "Existence of limit occupational measures set used for averaging of singularly perturbed controlled stochastic differential equations",

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.",

author = "Vivek Borkar and Vladimir Gaitsgory",

year = "2006",

language = "English",

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pages = "326--331",

booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "45th IEEE Conference on Decision and Control 2006, CDC ; Conference date: 13-12-2006 Through 15-12-2006",

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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., 4178126, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 326-331, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 13/12/06.

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

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - Existence of limit occupational measures set used for averaging of singularly perturbed controlled stochastic differential equations

AU - Borkar, Vivek

AU - Gaitsgory, Vladimir

PY - 2006

Y1 - 2006

N2 - 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.

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.

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AN - SCOPUS:39649108882

SN - 1424401712

SN - 9781424401710

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BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

T2 - 45th IEEE Conference on Decision and Control 2006, CDC

Y2 - 13 December 2006 through 15 December 2006

ER -

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

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