Guohuan Zhao

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math.PR2026

Persistence and local extinction for superprocesses in random environments

Zhen-Qing Chen, Yan-Xia Ren, Guohuan Zhao

We consider a super-Brownian motion ${X_{t}, t \geq 0}$ in a random environment described by a centered Gaussian field ${W (t, x), t \geq 0, x \in R^{d}}$ whose correlation funct…

math.PR2024

Quantitative estimates for SPDEs on the full space with transport noise and $L^{p}$ -initial data

Dejun Luo, Bin Xie, Guohuan Zhao

For the stochastic linear transport equation with $L^{p}$ -initial data ( $1 < p < 2$ ) on the full space $R^{d}$ , we provide quantitative estimates, in negative Sobolev norms, betwe…

math.PR2024

An elementary approach to mixing and dissipation enhancement by transport noise

Dejun Luo, Bin Tang, Guohuan Zhao

We investigate the mixing properties of solutions to the stochastic transport equation $d u = \circ d W \cdot \nabla u$ , where the driving noise $W (t, x)$ is white in time, colored an…

Persistence and local extinction for superprocesses in random environments

Quantitative estimates for SPDEs on the full space with transport noise and Lp-initial data

An elementary approach to mixing and dissipation enhancement by transport noise

Quantitative estimates for SPDEs on the full space with transport noise and $L^{p}$ -initial data