On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness

Abstract

Stochastic parabolic integro-differential problem is considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in Lp-spaces of functions whose regularity is defined by a scalable Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.