Self-intersection local times for generalized grey Brownian motion in higher dimensions

TL;DR

This paper establishes the mathematical foundation for self-intersection local times of generalized grey Brownian motion in higher dimensions, showing they are well-defined under certain conditions.

Contribution

It extends the theory of self-intersection local times to generalized grey Brownian motion in arbitrary dimensions, providing rigorous conditions for their existence.

Findings

Self-intersection local times are well-defined in distribution space for $deta<2$.

The work generalizes previous results to higher dimensions and broader classes of stochastic processes.

Provides a framework for analyzing complex stochastic behaviors in higher-dimensional systems.

Abstract

We prove that the self-intersection local times for generalized grey Brownian motion $B^{\beta,\alpha}$ in arbitrary dimension $d$ is a well defined object in a suitable distribution space for $d\alpha<2$.