Assouad dimension of random processes

TL;DR

This paper investigates the Assouad dimension of graphs of specific Lévy processes and stochastic integral functions, establishing conditions for full dimension and demonstrating their applicability to these processes.

Contribution

It introduces a new condition ensuring full Assouad dimension and proves that graphs of certain Lévy processes and stochastic integral functions meet this condition.

Findings

Graphs of studied processes have full Assouad dimension.

A new sufficient condition for full Assouad dimension is established.

The condition applies to Lévy processes and stochastic integral functions.

Abstract

In this paper we study the Assouad dimension of graphs of certain L\'evy processes and functions defined by stochastic integrals. We do this by introducing a convenient condition which guarantees a graph to have full Assouad dimension and then show that graphs of our studied processes satisfy this condition.