Continuous-time zero-sum games for markov decision processes with discounted risk-sensitive cost criterion on a general state space

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2021-12-21 DOI:10.1080/07362994.2021.2013889

Subrata Golui, Chandan Pal

引用次数: 0

Abstract

We consider zero-sum stochastic games for controlled continuous time Markov processes on a general state space with risk-sensitive discounted cost criteria. The transition and cost rates are possibly unbounded. Under a stability assumption, we prove the existence of a saddle-point equilibrium in the class of Markov strategies and give a characterization in terms of the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. Also, we illustrate our results and assumptions by an example.

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一般状态空间上具有折现风险敏感代价准则的马尔可夫决策过程的连续零和博弈

摘要考虑一般状态空间上具有风险敏感折现代价准则的可控连续时间马尔可夫过程的零和随机对策。转换率和成本率可能是无限的。在稳定性假设下，我们证明了一类马尔可夫策略的鞍点平衡点的存在性，并给出了相应的Hamilton-Jacobi-Isaacs (HJI)方程的表征。此外，我们还通过一个例子来说明我们的结果和假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.