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Strong well-posedness for cyclic catalytic reaction--diffusion SPDEs with mutation and immigration
Jie Xiong, Wen Xu
We study cyclic catalytic stochastic reaction-diffusion systems with mutation and immigration. The equations have square-root catalytic coefficients and spatially colored noise. Un…
Extinction and extinguishment properties for a nonlinear predator-prey branching model
Lina Ji, Jie Xiong, Wen Xu +1
We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populat…
Strong uniqueness and large deviation principle for mutually catalytic super Markov chains
Jie Xiong, Wen Xu
In this paper, we study the strong uniqueness problem for the mutually catalytic super-Markov chain, which is a two-dimensional degenerate stochastic differential equation with Höl…
Pathwise uniqueness for degenerate stochastic differential equations with Hölder continuous coefficients
Jie Xiong, Wen Xu
We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the…