Numerical solutions of optimal stopping problems for a class of hybrid stochastic systems

被引：0

作者：

Ernst P.A. ^{[1
]}

Ma X. ^{[2
]}

Nazari M.H. ^{[3
]}

Qian H. ^{[4
]}

Wang L.Y. ^{[3
]}

Yin G. ^{[2
]}

机构：

[1] Department of Mathematics, Imperial College London

[2] Department of Mathematics, University of Connecticut, Storrs, CT

[3] Department of Electrical & Computer Engineering, Wayne State University, Detroit, MI

[4] Department of Electrical and Computer Engineering, Cornell University, Ithaca, NY

来源：

Nonlinear Analysis: Hybrid Systems | 2024年 / 53卷

基金：

美国国家科学基金会;

关键词：

Markov chain approximation; Optimal stopping; Switching diffusions; Weak convergence;

D O I：

10.1016/j.nahs.2024.101507

中图分类号：

学科分类号：

摘要：

This paper is devoted to numerically solving a class of optimal stopping problems for stochastic hybrid systems involving both continuous states and discrete events. The motivation for solving this class of problems stems from quickest event detection problems of stochastic hybrid systems in broad application domains. We solve the optimal stopping problems numerically by constructing feasible algorithms using Markov chain approximation techniques. The key tasks we undertake include designing and constructing discrete-time Markov chains that are locally consistent with switching diffusions, proving the convergence of suitably scaled sequences, and obtaining convergence for the cost and value functions. Finally, numerical results are provided to demonstrate the performance of the algorithms. © 2024 Elsevier Ltd

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