Special Session 19: Stochastic Partial Differential Equations

A unified forward-backward Levy process driven SPDE and stochastic Differential Games

Wanyang Dai
Nanjing University
Peoples Rep of China
We establish a relationship between a unified forward-backward Levy process driven stochastic partial differential equation (SPDE) and stochastic differential games (SDGs). The SDGs are with q players and are driven by a general-dimensional vector Levy process. The unified forward-backward coupled SPDE is in both general dimensional vector-form and forward-backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position-parameters over a space domain. Since the unified SPDE is with general nonlinearity and general high-order, we extend our recently developed approach from the existing Brownian driven case to a general Levy driven case by constructing a new supporting topological space with the target to prove the unique existence of an adapted 4-tuple strong solution to the unified forward-backward SPDE under general local linear growth and Lipschitz conditions.