Semiconservative random walks in weak sense

TL;DR

This paper extends the concept of semiconservative random walks from integer lattices to continuous space, introducing and constructing such walks in weak sense in d space.

Contribution

It generalizes semiconservative random walks to d continuous space and provides a construction method for these walks in weak sense.

Findings

Introduction of semiconservative random walks in weak sense in d space

Construction of a family of such random walks in d space

Extension of previous discrete models to continuous setting

Abstract

Conservative and semiconservative random walks in $\mathbb{Z}^d$ were introduced and studied in [V.M. Abramov, J. Theor. Probab. (2017). https://doi.org/10.1007/s10959-017-0747-3]. In the present paper, we extend these concepts for random walks in $\mathbb{R}^d$ introducing semiconservative random walks in weak sense and construct such a family of random walks in $\mathbb{R}^d$.