DMS Stochastics Seminar

Speaker: Ms. Xiangqian Meng

Title:  Space-time fractional stochastic partial differential equations with Lévy Noise

Abstract:  We consider non-linear time-fractional  stochastic heat type equation with Poisson random measure or  compensated Poisson random measure. We prove existence and uniqueness of mild solutions to this equation. Our results  extend the results in the case of parabolic stochastic partial differential equations obtained before. Under some mild assumptions we show that solution of the time fractional stochastic partial differential equation grows  exponentially with respect to the time. We also establish the non-existence of the random field solution of both  of these stochastic partial differential equations under faster than linear growth of the drift coefficient.