71 citations · 352 across the 75 of their papers we have counts for
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Analysis of a Stratified Kraichnan Flow
Jingyu Huang, Davar Khoshnevisan
We consider the stochastic convection-diffusion equation \[ \partial_t u(t\,,{\bf x}) =νΔu(t\,,{\bf x}) + V(t\,,x_1)\partial_{x_2}u(t\,,{\bf x}), \] for and ${\bf x}=(x_1\,,x…
Talagrand Concentration Inequalities for Stochastic Partial Differential Equations
Davar Khoshnevisan, Andrey Sarantsev
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserste…
A macroscopic multifractal analysis of parabolic stochastic PDEs
Davar Khoshnevisan, Kunwoo Kim, Yimin Xiao
It is generally argued that the solution to a stochastic PDE with multiplicative noise---such as , where denotes space-time white noise---routinely produ…
On the multifractal local behavior of parabolic stochastic PDEs
Jingyu Huang, Davar Khoshnevisan
Consider the stochastic heat equation on subject to , where is a Lipschitz (local…
Dense blowup for parabolic SPDEs
Le Chen, Jingyu Huang, D. Khoshnevisan +1
The main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type $$ \partial_t u=\frac12Δu +σ(u)η\qquad\text{on…
Global solutions to reaction-diffusion equations with super-linear drift and multiplicative noise
Robert C. Dalang, Davar Khoshnevisan, Tusheng Zhang
Let denote space-time white noise and consider a reaction-diffusion equation of the form \[ \dot{u}(t\,,x)=\tfrac12 u"(t\,,x) + b(u(t\,,x)) + σ(u(t\,,x)) ξ(t\,,x), \] on…