2021/01/16 by Alessandro Bondi, Bondi, Alessandro
Economics, Econometrics and Finance · #47D07 #60E07 #60H15 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2101.06493
openalex publication_date 2021/01/16 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
We investigate the concept of cylindrical Wiener process subordinated to a strictly α-stable Lévy process, with α∈(0,1), in an infinite dimensional, separable Hilbert space, and consider the related stochastic convolution. We then introduce the corresponding Ornstein-Uhlenbeck process, focusing on the regularizing properties of the Markov transition semigroup defined by it. In particular, we provide an explicit, original formula -- which is not of Bismut-Elworthy-Li's type -- for the Gateaux derivatives of the functions generated by the operators of the semigroup, as well as an upper bound for the norm of their gradients. In the case α∈((1)/(2),1), this estimate represents the starting point for studying the Kolmogorov equation in its mild formulation.