Weak infinitesimal generator for a stochastic partialdifferential equation with time delay

[摘要] In this paper, we consider the Markov solution process for a stochastic parabolic differential equation with time delay. Under the Lipschitz condition and boundedness on the drift and diffusion coefficient, properties of the weak infinitesimal generator of the associated Markov operators are established. Actions of the weak infinitesimal generator on the space of quasi-tame functions are also investigated.

[学科分类] 应用数学