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

Author

Borkar, Vivek ; Gaitsgory, Vladimir

Author_Institution

Sch. of Technol. & Comput. Sci., Tata Inst. of Fundamental Res., Mumbai

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

326

Lastpage

331

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

Keywords

differential equations; infinite horizon; singularly perturbed systems; stochastic processes; stochastic systems; limit occupational measure; singularly perturbed controlled stochastic differential equations; time horizon; Convergence; Differential equations; Extraterrestrial measurements; H infinity control; Lakes; Nonlinear dynamical systems; Stochastic processes; Time measurement; Topology; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377570

Filename

4178126