29 citations · 77 across the 22 of their papers we have counts for
22 papers
Gaussian fluctuations for the wave equation under rough random perturbations
Raluca M. Balan, Jingyu Huang, Xiong Wang +2
In this article, we consider the stochastic wave equation in spatial dimension , with linear term multiplying the noise. This equation is driven by a Gaussian noise w…
Superlinear stochastic heat equation on
Le Chen, Jingyu Huang
In this paper, we study the stochastic heat equation (SHE) on subject to a centered Gaussian noise that is white in time and colored in space. We establish the exist…
Gaussian fluctuations for the stochastic heat equation with colored noise
Jingyu Huang, David Nualart, Lauri Viitasaari +1
In this paper, we present a quantitative central limit theorem for the d-dimensional stochastic heat equation driven by a Gaussian multiplicative noise, which is white in time and…
Regularity and strict positivity of densities for the stochastic heat equation on
Le Chen, Jingyu Huang
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity…
A Central Limit Theorem for the stochastic heat equation
Jingyu Huang, David Nualart, Lauri Viitasaari
We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from to conve…
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…
Chaos expansion of 2D parabolic Anderson model
Yu Gu, Jingyu Huang
We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the annealed density function of the polymer in…
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…
Spatial asymptotic of the stochastic heat equation with compactly supported initial data
Jingyu Huang, Khoa Lê
We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach infinity. The noise is white i…
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…
Parabolic Anderson model with rough dependence in space
Yaozhong Hu, Jingyu Huang, Khoa Lê +2
This paper studies the one-dimensional parabolic Anderson model driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst…
On stochastic heat equation with measure initial data
Jingyu Huang
The aim of this short note is to obtain the existence, uniqueness and moment upper bounds of the solution to a stochastic heat equation with measure initial data, without using the…
Delocalization of a -dimensional stochastic wave equation
Jingyu Huang, Davar Khoshnevisan
A noteworthy property of many parabolic stochastic PDEs is that they locally linearize (Foondun, Khoshnevisan and Mahboubi (2015), Hairer (2013, 2014), Hairer and Pardoux (2015), K…
Comparison principle for stochastic heat equation on
Le Chen, Jingyu Huang
We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on \[ \left(\frac{\partial }{\par…
Large time asymptotics for the parabolic Anderson model driven by space and time correlated noise
Jingyu Huang, Khoa Lê, David Nualart
We consider the linear stochastic heat equation on , driven by a Gaussian noise which is colored in time and space. The spatial covariance satisfies general assump…
Large time asymptotics for the parabolic Anderson model driven by spatially correlated noise
Jingyu Huang, Khoa Lê, David Nualart
In this paper we study the linear stochastic heat equation, also known as parabolic Anderson model, in multidimension driven by a Gaussian noise which is white in time and it has a…
Space-time fractional diffusions in Gaussian noisy environment
Le Chen, Guannan Hu, Yaozhong Hu +1
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^β+ \fracν{2} (-Δ)^{α/2} \right) u(t,x)=…
On the intermittency front of stochastic heat equation driven by colored noises
Yaozhong Hu, Jingyu Huang, David Nualart
We study the propagation of high peaks (intermittency front) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in . The n…
Stochastic heat equation with rough dependence in space
Yaozhong Hu, Jingyu Huang, Khoa Lê +2
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian mo…
Smoothness of the joint density for spatially homogeneous SPDEs
Yaozhong Hu, Jingyu Huang, David Nualart +1
In this paper we consider a general class of second order stochastic partial differential equations on driven by a Gaussian noise which is white in time and it has a…
Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
Yaozhong Hu, Jingyu Huang, David Nualart +1
This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both…
On Hölder continuity of the solution of stochastic wave equations
Yaozhong Hu, Jingyu Huang, David Nualart
In this paper, we study the stochastic wave equations in the spatial dimension 3 driven by a Gaussian noise which is white in time and correlated in space. Our main concern is the…