Low-dimensional Cox-Ingersoll-Ross process
Probability
2023-03-24 v1
Abstract
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square root of the CIR process. We utilize the fact that non-negative diffusion processes can be obtained by the transformation of time and scale of some reflected Brownian motion to derive this equation, which contains a term characterized by the local time of the corresponding reflected Brownian motion. Additionally, we establish a new connection between low-dimensional CIR processes and reflected Ornstein-Uhlenbeck (ROU) processes, providing a new representation of Skorokhod reflection functions.
Keywords
Cite
@article{arxiv.2303.12911,
title = {Low-dimensional Cox-Ingersoll-Ross process},
author = {Yuliya Mishura and Andrey Pilipenko and Anton Yurchenko-Tytarenko},
journal= {arXiv preprint arXiv:2303.12911},
year = {2023}
}