Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

TL;DR

This paper studies the conditions under which the squared Bessel and CIR processes with a reflection term at a deterministic, time-dependent curve exhibit pathwise uniqueness, extending understanding of these stochastic processes.

Contribution

It establishes pathwise uniqueness for squared Bessel and CIR processes with a reflection term scaled by a factor between -1 and 1, involving local time at a moving boundary.

Findings

Pathwise uniqueness holds under specified conditions.

Reflection at a time-dependent curve affects process behavior.

Results extend existing theory for reflected stochastic processes.

Abstract

We investigate pathwise uniqueness for the squared Bessel and Cox-Ingersoll-Ross processes with additional reflection term that is multiplied by some real number strictly between minus one and one. The reflection term is the symmetric local time of the corresponding processes at a deterministic time dependent curve.