4 papers · 1 filter
Hitting Probabilities for Hypoelliptic Differential Equations Driven by Fractional Brownian Motion
Xi Geng, Sheng Wang
The main goal of this article is to derive a two-sided estimate for hitting probabilities of a hypoelliptic stochastic differential equation (SDE) driven by fractional Brownian mot…
Parabolic Anderson Model in Hyperbolic Spaces and Phase Transition
Xi Geng, Cheng Ouyang
Consider a Parabolic Anderson model (PAM) with Gaussian noise that is white in time and colored in space, where the spatial correlation decays polynomially with order . In Eucli…
Parabolic Anderson Model in the Hyperbolic Space. Part I: Annealed Asymptotics
Xi Geng, Weijun Xu
We establish the second-order moment asymptotics for a parabolic Anderson model in the hyperbolic space with a regular, stationary Gaussian potential . It…
Parabolic Anderson Model in the Hyperbolic Space. Part II: Quenched Asymptotics
Xi Geng, Sheng Wang, Weijun Xu
We establish the exact quenched asymptotic growth of the solution to the parabolic Anderson model (PAM) in the hyperbolic space with a regular, stationary, time-independent Gaussia…