On the Cauchy problem for stochastic integro-differential equations with radially O-regularly varying Levy measure

TL;DR

This paper investigates the well-posedness of a class of stochastic integro-differential equations with Levy measures exhibiting O-regular variation, establishing existence, uniqueness, and probabilistic estimates.

Contribution

It introduces a framework for analyzing parabolic integro-differential equations with O-regularly varying Levy measures, providing new a priori estimates and solution criteria.

Findings

Existence and uniqueness of solutions in Lp spaces are proved.

A priori estimates for solutions are derived.

Probability density function estimates for Levy processes are obtained.

Abstract

Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some probability density function estimates of the associated Levy process are used as well.