Low-dimensional Cox-Ingersoll-Ross process

Yuliya Mishura; Andrey Pilipenko; Anton Yurchenko-Tytarenko

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arXiv · 2303.12911

Low-dimensional Cox-Ingersoll-Ross process

Yuliya Mishura·Andrey Pilipenko·Anton Yurchenko-Tytarenko

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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.

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Yuliya Mishura, Andrey Pilipenko, Anton Yurchenko-Tytarenko. 2023-03-22. Low-dimensional Cox-Ingersoll-Ross process. https://arxiv.org/abs/2303.12911

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