南方科技大学知识苑(SUSTech KC): A ZERO-SUM HYBRID STOCHASTIC DIFFERENTIAL GAME WITH SWITCHING CONTROLS

题名	A ZERO-SUM HYBRID STOCHASTIC DIFFERENTIAL GAME WITH SWITCHING CONTROLS
作者	Lv, Siyu 1; Xiong, Jie2,3
通讯作者	Xiong, Jie
发表日期	2024-03-01
DOI	10.3934/mcrf.2024007
发表期刊	MATHEMATICAL CONTROL AND RELATED FIELDS 影响因子和分区
ISSN	2156-8472
EISSN	2156-8499
摘要	In this paper, we study a zero-sum stochastic differential game in an infinite horizon, where the state equation consists of a number of diffusions coupled by a Markov chain and both players in the game employ switching controls. Based on the dynamic programming principle (DPP), the lower and upper value functions of the game are characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, which turns out to be two systems of variational inequalities with bilaterally inner-connected obstacles; thus the two value functions coincide and the game admits a value. Moreover, a verification theorem as a sufficient condition for Nash equilibriums is established, in which the equilibrium switching strategies for the two players are given in terms of the obstacle part of the HJBI equation.
关键词	Stochastic differential game markov chain switching control HJBI equation viscosity solution verification theorem
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	通讯
资助项目	National Key R&D Program of China[2022YFA1006102] ; National Natural Science Foundation of China["11801072","11831010"]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:001180127600001
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
来源库	Web of Science
引用统计
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/788888
专题	理学院_数学系南方科技大学
作者单位	1.Southeast Univ, Sch Math, Nanjing 211189, Peoples R China 2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 3.Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China
通讯作者单位	数学系; 南方科技大学
推荐引用方式 GB/T 7714	Lv, Siyu,Xiong, Jie. A ZERO-SUM HYBRID STOCHASTIC DIFFERENTIAL GAME WITH SWITCHING CONTROLS[J]. MATHEMATICAL CONTROL AND RELATED FIELDS,2024.
APA	Lv, Siyu,&Xiong, Jie.(2024).A ZERO-SUM HYBRID STOCHASTIC DIFFERENTIAL GAME WITH SWITCHING CONTROLS.MATHEMATICAL CONTROL AND RELATED FIELDS.
MLA	Lv, Siyu,et al."A ZERO-SUM HYBRID STOCHASTIC DIFFERENTIAL GAME WITH SWITCHING CONTROLS".MATHEMATICAL CONTROL AND RELATED FIELDS (2024).