Khoa Le

activity

20152022

most citedAsymptotics of the density of parabolic Anderson random fields

10 citations · 18 across the 7 of their papers we have counts for

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7 papers · 1 filter

math.PR2022★ 2 cited

Quantitative John--Nirenberg inequality for stochastic processes of bounded mean oscillation

Khoa Lê

Stroock and Varadhan in 1997 and Geiss in 2005 independently introduced stochastic processes with bounded mean oscillation (BMO) and established their exponential integrability wit…

math.PR2018

Joint Hölder continuity of parabolic Anderson model

Yaozhong Hu, Khoa Lê

We show that the random field solution to the parabolic Anderson equation $(\partial_{t} - \frac{1}{2} Δ) u = u ⋄ W ˙$ is jointly Hölder continuous in space and time.

math.PR2018★ 10 cited

Asymptotics of the density of parabolic Anderson random fields

Yaozhong Hu, Khoa Lê

We investigate the sharp density $ρ (t, x; y)$ of the solution $u (t, x)$ to stochastic partial differential equation $\frac{\partial }{\partial t} u(t,x)=\frac12 Δu(t,x)+u\diamond \do…

math.PR2017

Long-time asymptotic of stable Dawson-Watanabe processes in supercritical regimes

Khoa Lê

Let $W = (W_{t})_{t \geq 0}$ be a supercritical $α$ -stable Dawson-Watanabe process (with $α \in (0, 2]$ ) and $f$ be a test function in the domain of $- (- Δ)^{\frac{α}{2}}$ satisfying some i…

math.PR2017

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…

math.PR2015★ 1 cited

Stochastic Differential Equation for Brox Diffusion

Yaozhong Hu, Khoa Lê, Leonid Mytnik

This paper studies the weak and strong solutions to the stochastic differential equation $d X (t) = - \frac{1}{2} W ˙ (X (t)) d t + d B (t)$ , where $(B (t), t \geq 0)$ is a sta…