43 citations · 69 across the 13 of their papers we have counts for
13 papers
Stochastic fractional diffusion equations with Gaussian noise rough in space
Yuhui Guo, Jian Song, Xiaoming Song
In this article, we consider the following stochastic fractional diffusion equation \begin{equation*} \left(\partial^β+\dfracν{2}\left(-Δ\right)^{α/ 2}\right) u(t, x)= λ\: I_{0_+}^…
Spatial averages for the Parabolic Anderson model driven by rough noise
David Nualart, Xiaoming Song, Guangqu Zheng
In this paper, we study spatial averages for the parabolic Anderson model in the Skorohod sense driven by rough Gaussian noise, which is colored in space and time. We include the c…
Large deviation principles for stochastic dynamical systems with a fractional Brownian noise
Amarjit Budhiraja, Xiaoming Song
We study small noise large deviation asymptotics for stochastic differential equations with a multiplicative noise given as a fractional Brownian motion with Hurst parameter…
Fractional stochastic wave equation driven by a Gaussian noise rough in space
Jian Song, Xiaoming Song, Fangjun Xu
In this article, we consider fractional stochastic wave equations on driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of…
Large deviations for functionals of some self-similar Gaussian processes
Xiaoming Song
We prove large deviation principles for , where is a -dimensional self-similar Gaussian process and takes the form of the Dirac delta function $δ(x…
Nonlinear Feynman-Kac formulae for SPDEs with space-time noise
Jian Song, Xiaoming Song, Qi Zhang
We study a class of backward doubly stochastic differential equations (BDSDEs) involving martingales with spatial parameters, and show that they provide probabilistic interpretatio…