6 papers
Wick Renormalized Parabolic Stochastic Quantization Equations on Rough Metric Measure Spaces
Hongyi Chen, Yifan, Yang
On metric measure spaces with sub-Gaussian heat kernel behavior in small time, we obtain a sufficient condition to solve Wick renormalized stochastic quantization equations with po…
Propagation of Singularities for the Damped Stochastic Klein-Gordon Equation
Hongyi Chen, Cheuk Yin Lee
For the dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the sa…
Martin Boundary and Invariant Fields of Multiplicative SHE
Hongyi Chen
We study invariant measures of nonlinear multiplicative stochastic heat equations in the weak disorder regime. Under a natural second-moment condition, we show that positive invari…
Sharp Riemannian heat kernel estimates on the cut locus and the Parabolic Anderson model
Hongyi Chen, Robert Neel, Cheng Ouyang
Using sharp global heat kernel bounds and geodesic comparison geometry, we show that the Dalang condition for well-posedness of the parabolic Anderson model with measure-valued ini…
Global Geometry within an SPDE Well-Posedness Problem
Hongyi Chen, Cheng Ouyang
On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter to study the well-posedness of the parabolic Anderso…
Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds
Fabrice Baudoin, Hongyi Chen, Cheng Ouyang
We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in sp…