Non-local Operators, Non-Archimedean Parabolic-type Equations with Variable Coefficients and Markov Processes

Abstract

In this article, we introduce a new class of parabolic-type pseudodifferential equations with variable coefficients over the $p$-adics. We establish the existence and uniqueness of solutions for the Cauchy problem associated with these equations. The fundamental solutions of these equations are connected with Markov processes. Some of these equations are related to new models of complex systems.