# The small deviations of many-dimensional diffusion processes and rarefaction by boundaries

## TL;DR

This paper develops an expansion algorithm for the sojourn probability of high-dimensional diffusion processes in small domains, which aids in establishing limit theorems by defining a key normalizing coefficient.

## Contribution

It introduces a novel expansion algorithm for the sojourn probability in many-dimensional diffusion processes, facilitating new limit theorems.

## Key findings

- Derived the principal term of the expansion as a normalizing coefficient
- Established connections between the expansion and limit theorems
- Provided a method for analyzing boundary effects in diffusion processes

## Abstract

We lead the algorithm of expansion of sojourn probability of many-dimensional diffusion processes in small domain. The principal member of this expansion defines normalizing coefficient for special limit theorems.