# Intersection local time for two independent fractional Brownian motions

## TL;DR

This paper establishes the conditions under which the intersection local time exists for two independent fractional Brownian motions, specifically when their dimensions and Hurst parameters satisfy Hd<2.

## Contribution

It proves the existence of intersection local time for two independent fractional Brownian motions with the same Hurst parameter, extending understanding of their intersection properties.

## Key findings

- Intersection local time exists if and only if Hd<2.
- Existence is proven for dimensions d≥2 and Hurst parameter H.
- Provides a precise condition linking dimension and Hurst parameter.

## Abstract

We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the intersection local time exists if and only if Hd<2.