Continuous-Time Random Walk Approach to Modeling of Relaxation: The Role of Compound Counting Processes

摘要

We propose a diffusion, continuous-time random walk (CTRW) scenario which is based on generalization of processes counting the number of jumps performed by a walker. We substitute the renewal counting process, used in the classical CTRW framework, by a compound counting process. The construction of such a compound process involves renormalized clustering of random number of walker’s spatio-temporal subsequent steps. The family of the renormalized steps defines a new class of coupled CTRWs. The diffusion front of the studied process exhibits properties which help us to enlarge the class of relaxation models discussed yet in the classical CTRW framework.