Some quenched and annealed limit theorems for superprocesses in random environments

Zeteng Fan, Jieliang Hong and Jie Xiong

Stochastic Processes and their Applications, 2025, vol. 188, issue C

Abstract: Let X=(Xt,t≥0) be a superprocess in a random environment described by a Gaussian noise W={W(t,x),t≥0,x∈Rd} white in time and colored in space with correlation kernel g(x,y). When d≥3, under the condition that the correlation function g(x,y) is bounded above by some appropriate function ḡ(x−y), we present the quenched and annealed Strong Law of Large Numbers and the Central Limit Theorems regarding the weighted occupation measure ∫0tXsds as t→∞.

Keywords: Superprocess; Stochastic partial differential equation; Random environment (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104686

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