Strong solutions to beta-Jacobi processes

TL;DR

This paper investigates the existence and uniqueness of strong solutions to a system of SDEs modeling beta-Jacobi processes, focusing on boundary behavior and conditions preventing finite-time collisions.

Contribution

It establishes conditions for strong, pathwise unique solutions to beta-Jacobi SDEs and analyzes boundary collision phenomena.

Findings

Existence of strong solutions until boundary collision.

Conditions ensuring solutions do not hit boundaries in finite time.

Analysis of Coulombian-like repulsion effects.

Abstract

The purpose of this paper is to study the existence and uniqueness of solutions to a system of Stochastic Differential Equations (SDEs). The coordinates are bounded by zero and one, and repulse each other according to a Coulombian like interaction force. We show the existence of strong and pathwise unique solutions to the system until the first multiple collision at zero or one, and give a sufficient condition on the parameters of the SDEs for this multiple collision not to occur in finite time.