Fei Pu

activity

20122026

most citedSpatial ergodicity for SPDEs via a Poincaré-type inequality

13 citations · 39 across the 20 of their papers we have counts for

collaborators

20 papers

math.PR2026

Two-time spatial decorrelation for the flat KPZ fixed point

Le Chen, Fei Pu

We establish quantitative two-time spatial decorrelation for the Kardar--Parisi--Zhang fixed point with flat initial data. For every $s, t > 0$ ,there exist constants $C, c > 0$ such that…

math.PR2025

Uniform dimension theorems for parabolic SPDEs

Davar Khoshnevisan, Cheuk Yin Lee, Fei Pu +1

Consider the following $p$ -dimensional system of Itô type stochastic PDEs, \begin{align*}\left[\begin{aligned} &\partial_t u(t\,,x) = \partial^2_x u(t\,,x) + b(u(t\,,x)) + σ(u(t\,,…

math.PR2025

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line

Robert C. Dalang, David Nualart, Fei Pu

For Gaussian random fields with values in $R^{d}$ , sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in…

math.PR2023

Lower bound on spatial asymptotic of parabolic Anderson model with narrow wedge initial condition

Fei Pu

Let ${u (t, x) : (t, x) \in (0, \infty) \times R}$ be the solution to parabolic Anderson model with narrow wedge initial condition. Using the association property of parabol…

math.PR2023

Ergodicity, CLT and asymptotic maximum of the Airy $_{1}$ process

Fei Pu

We first show that the Airy $_{1}$ process is associated using the association property of the solution to the stochastic heat equation and convergence of the KPZ equation to the KPZ…

math.PR2023

Hitting with probability one for stochastic heat equations with additive noise

Robert C. Dalang, Fei Pu

We study the hitting probabilities of the solution to a system of $d$ stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any b…

math.PR2021

Gaussian fluctuation for spatial average of super-Brownian motion

Zenghu Li, Fei Pu

Let ${u (t, x)}_{(t, x) \in R_{+} \times R}$ be the density of one-dimensional super-Brownian motion starting from Lebesgue measure. Using the Laplace functional o…

math.PR2021★ 2 cited

Gaussian fluctuation for Gaussian Wishart matrices of overall correlation

Ivan Nourdin, Fei Pu

In this note, we study the Gaussian fluctuations for the Wishart matrices $d^{- 1} X_{n, d} X_{n, d}^{T}$ , where $X_{n, d}$ is a $n \times d$ random matri…

math.PR2020★ 7 cited

Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method

Le Chen, Davar Khoshnevisan, David Nualart +1

Suppose that ${u (t, x)}_{t > 0, x \in R^{d}}$ is the solution to a $d$ -dimensional stochastic heat equation driven by a Gaussian noise that is white in time and has a spat…

math.PR2020★ 1 cited

Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions

Fei Pu

Consider the parabolic Anderson model $\partial_{t} u = \frac{1}{2} \partial_{x}^{2} u + u η$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space…

math.PR2020

Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension $d \geq 1$

Davar Khoshnevisan, David Nualart, Fei Pu

Suppose that ${u (t, x)}_{t > 0, x \in R^{d}}$ is the solution to a $d$ -dimensional parabolic Anderson model with delta initial condition and driven by a Gaussian noise tha…

math.PR2020★ 7 cited

Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition

Le Chen, Davar Khoshnevisan, David Nualart +1

Let ${u (t, x)}_{t > 0, x \in R}$ denote the solution to the parabolic Anderson model with initial condition $δ_{0}$ and driven by space-time white noise on $\mathbb{R}_+\t…

math.PR2020★ 2 cited

A CLT for dependent random variables, with an application to an infinite system of interacting diffusion processes

Le Chen, Davar Khoshnevisan, David Nualart +1

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem…

math.PR2019★ 3 cited

Central limit theorems for parabolic stochastic partial differential equations

Le Chen, Davar Khoshnevisan, David Nualart +1

Let ${u (t, x)}_{t \geq 0, x \in R^{d}}$ denote the solution of a $d$ -dimensional nonlinear stochastic heat equation that is driven by a Gaussian noise, white in time with a…

math.PR2019★ 1 cited

Spatial ergodicity for SPDEs via Poincaré-type inequalities

Le Chen, Davar Khoshnevisan, David Nualart +1

Consider a parabolic stochastic PDE of the form $\partial_{t} u = \frac{1}{2} Δ u + σ (u) η$ , where $u = u (t, x)$ for $t \geq 0$ and $x \in R^{d}$ , $σ : R \to R$ is…

math.PR2019★ 13 cited

Spatial ergodicity for SPDEs via a Poincaré-type inequality

Le Chen, Davar Khoshnevisan, Fei Pu

Consider a parabolic stochastic PDE of the form $\partial_{t} u = \frac{1}{2} Δ u + σ (u) η$ , where $u = u (t, x)$ for $t \geq 0$ and $x \in R^{d}$ , $σ : R \to R$ is Lipschit…

math.PR2018

On the density of the supremum of the solution to the linear stochastic heat equation

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of…

math.PR2018

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension $k \geq 1$

Robert Dalang, Fei Pu

We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix $γ_{Z}$ of $Z := (u (s, y), u (t, x) - u (s, y))$ , where $u$ is the solution to…

math.PR2018★ 3 cited

Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations

Robert C. Dalang, Fei Pu

We consider a system of $d$ non-linear stochastic fractional heat equations in spatial dimension $1$ driven by multiplicative $d$ -dimensional space-time white noise. We establish a…

math.PR2012

Strong solutions of jump-type stochastic equations

Zenghu Li, Fei Pu

We establish the existence and uniqueness of strong solutions to some jump-type stochastic equations under non-Lipschitz conditions. The results improve those of Fu and Li (2010) a…

Two-time spatial decorrelation for the flat KPZ fixed point

Uniform dimension theorems for parabolic SPDEs

Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line

Lower bound on spatial asymptotic of parabolic Anderson model with narrow wedge initial condition

Ergodicity, CLT and asymptotic maximum of the Airy1​ process

Hitting with probability one for stochastic heat equations with additive noise

Gaussian fluctuation for spatial average of super-Brownian motion

Gaussian fluctuation for Gaussian Wishart matrices of overall correlation

Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein's method

Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions

Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension d≥1

Spatial ergodicity and central limit theorems for parabolic Anderson model with delta initial condition

A CLT for dependent random variables, with an application to an infinite system of interacting diffusion processes

Central limit theorems for parabolic stochastic partial differential equations

Spatial ergodicity for SPDEs via Poincaré-type inequalities

Spatial ergodicity for SPDEs via a Poincaré-type inequality

On the density of the supremum of the solution to the linear stochastic heat equation

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k≥1

Optimal lower bounds on hitting probabilities for non-linear systems of stochastic fractional heat equations

Strong solutions of jump-type stochastic equations

Ergodicity, CLT and asymptotic maximum of the Airy $_{1}$ process

Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension $d \geq 1$

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension $k \geq 1$