### Speaker

### Description

A classical problem in ergodic control theory consists in the study of the limit behaviour of

λV λ (·) as λ ↘ 0, when V λ is the value function of a deterministic or stochastic control problem

with discounted cost functional with infinite time horizon and discount factor λ. We study this

problem for the lower value function V λ 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).