5 papers
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…
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 Eucl…
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 .…
Stochastic Domination of Exit Times for Random Walks and Brownian Motion with Drift
Xi Geng, Greg Markowsky
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stocha…