Ultrametric Diffusion, Exponential Landscapes, and the First Passage Time Problem

Abstract

In this article we study certain ultradiffusion equations connected with energy landscapes of exponential type. These equations are connected with the p-adic models of complex systems introduced by Avetisov et al. We show that the fundamental solutions of these equations are transition density functions of Lévy processes, we also study some aspects of these processes including the first passage time problem.

Minor revisions. Final version accepted in Acta Applicandae Mathematicae

References in corpus (1)

• Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks

Cited by in corpus (1)

• Non-Archimedean Reaction-Ultradiffusion Equations and Complex Hierarchic Systems