Large deviation principle for generalized multiple intersection local times of multidimensional Brownian motion

TL;DR

This paper establishes a large deviation principle for the generalized multiple intersection local times of multidimensional Brownian motion, providing insights into the probabilities of rare events in complex stochastic processes.

Contribution

It introduces a large deviation framework for generalized intersection local times of multidimensional Brownian motion, extending existing theories to more general Wiener functions.

Findings

Large deviation principle proven for generalized intersection local times.

Applicable to multidimensional Brownian motion with generalized Wiener functions.

Provides theoretical foundation for analyzing rare events in stochastic intersections.

Abstract

In this paper we consider examples of positive generalized Wiener functions and we establish a large deviation principle for the generalized multiple intersection local time of the multidimensional Brownian motion.