Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

TL;DR

This paper investigates a coupled continuous time random walk model with correlated jumps and waiting times, deriving space-time fractional diffusion equations and analyzing their asymptotic behaviors in Fourier-Laplace space.

Contribution

It introduces a novel coupled CTRW model with correlated jumps and waiting times, deriving associated fractional diffusion equations and analyzing their asymptotic properties.

Findings

Derived fractional diffusion equations from asymptotic behaviors.

Analyzed joint probability density functions in Fourier-Laplace space.

Discussed asymptotic behaviors of waiting time and jump length distributions.

Abstract

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.