Fractional diffusion in Gaussian noisy environment

الأصل · EN

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+u· Wʰ, where Dₜα is the fractional derivative of order α with respect to the time variable t, B is a second order elliptic operator with respect to the space variable xᵈ, and Wʰ a fractional Gaussian noise of Hurst parameter H=(H₁,, Hd). We obtain conditions satisfied by α and H so that the square integrable solution u exists uniquely.