Some singular sample path properties of a multiparameter fractional Brownian motion

TL;DR

This paper establishes a Chung-type law of the iterated logarithm for a multiparameter fractional Brownian motion, revealing unique path properties and fractal dimensions that differ from classical models.

Contribution

It introduces a Chung-type law for a non-increment stationary multiparameter fractional Brownian motion and analyzes its path and fractal properties.

Findings

Different behavior at the origin and away from axes

Hausdorff dimension of the range varies with location

Functional version of the Chung-type law provided

Abstract

We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the fractional Brownian motion which is not increment stationary. This multiparameter fractional Brownian motion behaves very differently at the origin and away from the axes, which also appears in the Hausdorff dimension of its range and in the measure of its pointwise H\"older exponents. A functional version of this Chung-type law is also provided.