Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 2 de mayo de 2019
Hora  : 12:00
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Petr Coupek

(Charles University of Prague)

Resumen

In deterministic calculus, the chain rule is one of the fundamental tools used for rigorous mathematical treatment of various models of physical phenomena. Very often, however, these models involve some sort of randomness, or noise, that is highly irregular and whose presence renders the usual tools (such as the chain rule) inapplicable. The talk will be devoted to Itô-type formulas for functionals of various stochastic processes. As motivation, we will talk about differential equations perturbed by noise and then we will review the already classical results on stochastic chain rules for the Wiener process and fractional Brownian motions. The main focus will be on some recent results on a stochastic chain rule for Rosenblatt processes. Rosenblatt processes are continuous stochastic processes that exhibit self-similarity and long memory; however, unlike fractional Brownian motions, they are not Gaussian. This last property makes their analysis somewhat intriguing and it is also the reason why they received considerable attention in the past couple of years.