| Abstract: |
| \begin{document}
\title{Representation of limit values for nonexpansive
stochastic differential games }
\author{ Juan Li\
{\small School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, P. R. China.}\
{\small{\it E-mail: juanli@sdu.edu.cn.}}
\date{ } }
\maketitle
\begin{abstract}
A classical problem in ergodic control theory consists in the study of the limit behaviour of $\lambda V_\lambda(\cdot)$ as $\lambda\searrow 0,$ when $V_\lambda$ is the value function of a deterministic or stochastic control problem with discounted cost functional with infinite time horizon and discount factor $\lambda$. We study this problem for the lower value function $V_\lambda$ of a stochastic differential game with recursive cost, i.e., the cost functional is defined through a backward stochastic differential equation with infinite time horizon. But unlike the ergodic control approach, we are interested in the case where the limit can be a function depending on the initial condition. For this we extend the so-called non-expansivity assumption from the case of control problems to that of stochastic differential games.
Based on a joint work with Rainer Buckdahn (Brest, France), Nana Zhao (Weihai, China).
\bigskip
\end{abstract}
\end{document} |
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