Deterministic approximation for stochastic control problems

R. Sh Liptser; W. J. Runggaldier; M. Taksar

doi:10.1137/S0363012993254540

Deterministic approximation for stochastic control problems

R. Sh Liptser^*
, W. J. Runggaldier
, M. Taksar

^*Corresponding author for this work

Engineering General

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise "intensity" is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem is asymptotically optimal for the stochastic problems.

Original language	English
Pages (from-to)	161-178
Number of pages	18
Journal	SIAM Journal on Control and Optimization
Volume	34
Issue number	1
DOIs	https://doi.org/10.1137/S0363012993254540
State	Published - Jan 1996

Keywords

Asymptotic optimality
Stochastic and deterministic control
Stochastic differential equations
Weak convergence

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10.1137/S0363012993254540

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AU - Taksar, M.

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AB - We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise "intensity" is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem is asymptotically optimal for the stochastic problems.

KW - Asymptotic optimality

KW - Stochastic and deterministic control

KW - Stochastic differential equations

KW - Weak convergence

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Deterministic approximation for stochastic control problems

Abstract

Keywords

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