@article{Liu2025, 
author = {Yueying Liu and Mengping Sun and Zhen Wang and Xiangyun Lin and Cuihua Zhang},
title = {Nash equilibrium strategies for non-zero-sum differential games of SDEs with time-varying coefficient and infinite Markov jumps},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {4},
pages = {2525-2542},
keywords = {stochastic differential equations, infinite Markov jumps, non-zero-sum Nash differential games, countable coupled generalized differential Riccati equations, unified treatment},
url = {https://www.sciopen.com/article/10.3934/era.2025112},
doi = {10.3934/era.2025112},
abstract = {This paper mainly discusses the non-zero-sum Nash differential games for stochastic differential equations (SDEs) involving time-varying coefficient and infinite Markov jumps. First of all, a necessary and sufficient conditions for the existence of Nash equilibrium strategies is given, which turns the non-zero-sum Nash differential games into solving the equations that are composed of countable coupled generalized differential Riccati equations (CGDREs). As an application, a unified treatment is presented for        H          2      ,        H          ∞      , and        H          2            /        H          ∞       control by the Nash game approach, which can reveal the relationship among these three problems. Furthermore, the theoretical results are used to solve a numerical example.}
}