In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...

In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^k(t,x)\delta {\beta }_t^k,t\in [0,T]$, with random coefficientsf and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.

In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))\mathrm{d}t+{\sum }_{k=1}^{\infty }{g}^k(t,x)\delta {\beta }_t^k,t\in [0,T]$, with random coefficients f and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.