4 papers · 1 filter
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…
Averaging principle for two time-scale stochastic differential equations with fast component in noncompact space
Shen Wang, Jinghai Shao
The asymptotic behavior for fully coupled multiscale stochastic systems becomes much complicated when the fast processes do not locate in a compact space. An example is constructed…
Cartan's Path Development, the Logarithmic Signature and a Conjecture of Lyons-Sidorova
Horatio Boedihardjo, Xi Geng, Sheng Wang
The signature transform, which is defined in terms of iterated path integrals of all orders, provides a faithful representation of the group of tree-reduced geometric rough paths.…