We are pleased to announce the PhD course "Bessel, Cox-Ingersoll-Ross, Ornstein-Uhlenbeck and Gaussian-Volterra processes with Wiener and fractional drivers", held by Prof. Yuliia Mishura (Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv)

The course is organized by the Doctoral Program in Mathematical Sciences of the University of Padova

---------------------

Aim: To introduce PhD students to the most interesting and modern models of stochastic pro- cesses, which, firstly, have various and quite deep analytical, wise-trajectory and asymptotic properties, and secondly, serve as adequate models in financial mathematics, physics, cellular communications, biology, etc. We will consider stochastic differential equations with both the Wiener process and the fractional Brownian process and its generalizations.

Course contents: Standard Cox-Ingersoll-Ross and Bessel processes: local and global be- haviour of the trajectories as the functionals of coefficients. Fractional Cox-Ingersoll-Ross and Bessel processes and their main properties in dependence of the value of Hurst index. Drift parameters estimation in the standard and fractional Cox-Ingersoll-Ross models. Exact and ap- proximate option pricing under stochastic volatility modeled by fractional Ornstein-Uhlenbeck process. Functional limit theorems for financial markets driven by fractional long-range de- pendent processes. Fractional Gaussian noise: entropy and alternative entropy functionals, an- alytical and computational problems related to predictors. Gaussian-Volterra processes as the generalization of fractional Brownian motion. Tempered fractional processes.

A more detailed description of the course can be found here:

https://www.math.unipd.it/~dottmath/corsi2025/Mishura.pdf

---------------------------

The course will consist of 16 hours, beginning on May 14, 2025 with the following calendar:

14/5 h. 14.30-16.30 16/5 h. 10.00-12.00 20/5 h. 14.30-16.30 21/5 h. 14.30-16.30 27/5 h. 14.30-16.30 30/5 h. 10.00-12.00 3/6 h. 14.30-16.30 6/6 h. 10.00-12.00

The course is free, but for organizing reasons we kindly ask all interested people to enroll the course here:

https://servizi-esterno.math.unipd.it/userlist/lista/view?id=119

------------------

Best regards Tiziano

-------------------------------------------------------------------------- Tiziano Vargiolu Dipartimento di Matematica Phone: +39 049 8271383 Universita' di Padova Fax: +39 049 8271428 Via Trieste, 63 E-mail: vargiolu@math.unipd.it I-35121 Padova (Italy) WWW: http://www.math.unipd.it/~vargiolu --------------------------------------------------------------------------