Some quenched and annealed limit theorems of superprocesses in random environments

2024/06/11 by Fan, Zeteng, Hong, Jieliang, Xiong, Jie
#60G57 #60H15 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2406.06905

Abstract

Let X=(X_t, t≥ 0) be a superprocess in a random environment described by a Gaussian noise W=\W(t,x), t≥ 0, x∈ ℝ^d\ 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 g(x-y), we present the quenched and annealed Strong Law of Large Numbers and the Central Limit Theorems regarding the weighted occupation measure ∫₀^t X_s ds as t→ ∞.

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