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

TL;DR

This paper investigates ultradiffusion equations related to exponential energy landscapes, linking them to p-adic models and Lévy processes, and explores their fundamental solutions and first passage time properties.

Contribution

It establishes the connection between ultradiffusion equations and Lévy processes, providing new insights into their fundamental solutions and first passage time analysis.

Findings

Fundamental solutions are transition densities of Lévy processes

Connection established between ultradiffusion equations and p-adic models

Analysis of first passage time problem for these processes

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 L\'evy processes, we also study some aspects of these processes including the first passage time problem.