Fractional diffusion in Gaussian noisy environment


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

    Similar works