Some stochastic time-fractional diffusion equations with variable coefficients and time dependent noise

2016/05/06 by Guannan Hu, Hu, Guannan
Economics, Econometrics and Finance · Computer Science · Engineering · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1605.01831

Abstract

We prove the existence and uniqueness of mild solution for the stochastic partial differential equation (∂^α- B ) u(t,x)= u(t,x) ⋅ W(t,x), where α∈ (1/2, 1)∪(1, 2); B is an uniform elliptic operator with variable coefficients and W is a Gaussian noise general in time with space covariance given by fractional, Riesz and Bessel kernel.

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