Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition

Yuliya Mishura; Kostiantyn Ralchenko; Svitlana Kushnirenko

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arXiv · 2410.13231

Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition

Yuliya Mishura·Kostiantyn Ralchenko·Svitlana Kushnirenko

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Abstract

This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to be a phase transition of the CIR process and can be approximated by a sequence of CIR processes. Differences in stochastic stability are also highlighted, with the Bessel process displaying instability, while the CIR process remains ergodic and stable.

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Yuliya Mishura, Kostiantyn Ralchenko, Svitlana Kushnirenko. 2024-10-17. Driven by Brownian motion Cox-Ingersoll-Ross and squared Bessel processes: interaction and phase transition. https://arxiv.org/abs/2410.13231

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