Random time-change with inverses of multivariate subordinators: governing equations and fractional dynamics

2019/12/19 by Luisa Beghin, Beghin, Luisa, Claudio Macci +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #Random time-change #anomalous diffusion #continuous time random walks #fractional operators #math.PR #multivariate Levy processes #subordinators

paper · pdf · doi:10.48550/arxiv.1912.09432

24 pages

arxiv created 2020/05/12 · arxiv updated 2020/05/13

Abstract

It is well-known that compositions of Markov processes with inverse subordinators are governed by integro-differential equations of generalized fractional type. This kind of processes are of wide interest in statistical physics as they are connected to anomalous diffusions. In this paper we consider a generalization; more precisely we mean componentwise compositions of ℝ^d-valued Markov processes with the components of an independent multivariate inverse subordinator. As a possible application, we present a model of anomalous diffusion in anisotropic medium, which is obtained as a weak limit of suitable continuous-time random walks.

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