CS30: Gaussian Processes for Fractional Dynamics and Limiting Behaviour

Organizer: Barbara Martinucci & Enrica Pirozzi (Salerno & Campania Luigi Vanvitelli)

Fractional rough diffusion Bessel processes: reflection, asymptotic behavior and parameter estimation

Yuliya Mishura

This is a common talk with K. Ralchenko and A. Yurchenko-Tytarenko. We consider fractional stochastic differential equations that recreate Cox-Ingersoll-Ross, Ornstein-Uhlenbeck and Bessel dynamics. The form of the equations can be different for big (\(H\in(1/2,1)\)) and small (\(H\in(0,1/2)\)) values of Hurst index \(H\). In the rough case reflection functions for CIR and Bessel dynamics participate. We establish the asymptotic in time behaviour of the solution and the reflection. Statistical parameter estimation is provided. The results are presented in \([1-4]\).

Bibliography

\([1]\) Mishura, Y., Ralchenko, K. Fractional diffusion Bessel processes with Hurst index \(H\in(0, 1/2)\). Statistics and Probability Letters, 206, 110008, 2024, pp.1–8.

\([2]\) Mishura, Y., Yurchenko-Tytarenko, A. Parameter estimation in rough Bessel model. Fractal and Fractional, 7(7), 508, 2023, pp. 1–17. Jane Smith. "Title of the Article." Journal Name, vol. X, no. Y, Year, pp. Z.

\([3]\) Mishura, Y., Yurchenko-Tytarenko, A. Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes. Stochastics, 95(1), 2023, pp. 99-117.

\([4]\) Ascione, G., Mishura, Y., Pirozzi, E. (2023). Fractional deterministic and stochastic calculus (Vol. 4). Walter de Gruyter GmbH & CoKG.