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February, 1991 Forcing a Stochastic Process to Stay in or to Leave a Given Region
Mario Lefebvre
Ann. Appl. Probab. 1(1): 167-172 (February, 1991). DOI: 10.1214/aoap/1177005986

Abstract

Systems defined by dx(t)=a[x(t),t]dt+B[x(t),t]u(t)dt+N1/2[x(t),t]dW(t), where x(t) is the state variable, u(t) is the control variable, a is a vector function, B and N are matrices and W(t) is a Brownian motion process, are considered. The aim is to minimize the expected value of a cost function with quadratic control costs on the way and terminal cost function K(T), where T=inf{s:x(s)Dx(t)=x},D being a given region in Rn. The function K is taken to be 0 if T()τ, where τ is a positive constant and + if T<(>)τ when the aim is to force x(t) to stay in (resp., to leave) the region C, the complement of D. A particular one-dimensional problem is solved explicitly and a risk-sensitive version of the general problem is also considered.

Citation

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Mario Lefebvre. "Forcing a Stochastic Process to Stay in or to Leave a Given Region." Ann. Appl. Probab. 1 (1) 167 - 172, February, 1991. https://doi.org/10.1214/aoap/1177005986

Information

Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0728.93078
MathSciNet: MR1097469
Digital Object Identifier: 10.1214/aoap/1177005986

Subjects:
Primary: 93E20
Secondary: 60J70

Keywords: Brownian motion , optimal control , risk sensitivity , Stochastic control

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 1 • February, 1991
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