On the model of random walk with multiple memory structure

Abstract

A model of one-dimensional random walk based on the memory flow phenomenology is constructed. In this model, the jumps of the random walk process have a convolution structure formed on the basis of a finite sequence of memory functions and a stationary, generally speaking, non-Gaussian sequence. A physical interpretation of memory functions and the stationary sequence is given. A limit theorem in the metric space D[0,1] for the normalized walk process is obtained.