About Speakers Schedule INS
反问题与不确定性量化研讨会 (Workshop on Inverse Problems and Uncertainty Quantification)

An inverse source problem for multi-term time-fractional stochastic differential equations driven by a fractional Brownian motion

Speaker

王旭 , 中国科学院数学与系统科学研究院

Time

18 Nov, 11:10 - 11:40

Abstract

In this talk, I will introduce an inverse source problem for the multi-term time-fractional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H\in (0,1)$. For the direct problem, the multi-term time-fractional stochastic differential equation is proved to admit a unique mild solution. For the inverse problem, we prove that the variance of the boundary data over the whole time domain can be used to uniquely determine the modulus of the Fourier modes of the diffusion coefficient involved in the random source. To further get the diffusion coefficient from its phaseless Fourier modes, the PhaseLift method combined with spectral cut-off technique is used to recover the modulus of diffusion coefficient numerically. Several numerical experiments are also reported to demonstrate the effectiveness of the proposed method.