205 research outputs found

    Fractional diffusion in Gaussian noisy environment

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    We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: Dtαu(t,x)=Bu+uWHD_t^\alpha u(t, x)=\textit{B}u+u\cdot W^H, where DtαD_t^\alpha is the fractional derivative of order α\alpha with respect to the time variable tt, B\textit{B} is a second order elliptic operator with respect to the space variable xRdx\in\mathbb{R}^d, and WHW^H a fractional Gaussian noise of Hurst parameter H=(H1,,Hd)H=(H_1, \cdots, H_d). We obtain conditions satisfied by α\alpha and HH so that the square integrable solution uu exists uniquely

    Stochastic integral representation of the L2L^{2} modulus of Brownian local time and a central limit theorem

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    The purpose of this note is to prove a central limit theorem for the L2L^2-modulus of continuity of the Brownian local time obtained in \cite{CLMR}, using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's theorem and the Clark-Ocone formula for the L2L^2-modulus of the Brownian local time