Holder continuity and occupation-time formulas for fBm self-intersection local time and its derivative

TL;DR

This paper establishes Holder continuity and occupation-time formulas for the self-intersection local time of fractional Brownian motion, introducing a new derivative process and analyzing its properties.

Contribution

It provides new joint Holder continuity results and a novel derivative of self-intersection local time for fractional Brownian motion, expanding theoretical understanding.

Findings

Proved joint Holder continuity of self-intersection local time

Derived occupation-time formula for fractional Brownian motion

Introduced and analyzed a new derivative process related to self-intersection local time

Abstract

We prove joint Holder continuity and an occupation-time formula for the self-intersection local time of fractional Brownian motion. Motivated by an occupation-time formula, we also introduce a new version of the derivative of self-intersection local time for fractional Brownian motion and prove Holder conditions for this process. This process is related to a different version of the derivative of self-intersection local time studied by the authors in a previous work.