Browsing by Subject "Malliavin calculus"

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  • Huang, Jingyu; Nualart, David; Viitasaari, Lauri (2020)
    We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from -R to R converges in total variance distance to a standard normal distribution as R tends to infinity, after renormalization. We also show a functional version of this central limit theorem. (C) 2020 Elsevier B.V. All rights reserved.
  • Azmoodeh, Ehsan; Gasbarra, Dario (2019)
    In this paper, using the Stein operator R-infinity given in [17], associated with the normal product distribution living in the second Wiener chaos, we introduce a new class of polynomials P-infinity:= {P-n(x) = R(infinity)(n)1 : n >= 1}. We analyze in details the polynomials class P-infinity, and relate it to Rota's Umbral calculus by showing that it is a Sheffer family and enjoys many interesting properties. Lastly, we study the connection between the polynomial class P-infinity and the non-central probabilistic limit theorems within the second Wiener chaos.