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Some quenched and annealed limit theorems for superprocesses in random environments

Author

Listed:
  • Fan, Zeteng
  • Hong, Jieliang
  • Xiong, Jie

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→∞.

Suggested Citation

  • Fan, Zeteng & Hong, Jieliang & Xiong, Jie, 2025. "Some quenched and annealed limit theorems for superprocesses in random environments," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001279
    DOI: 10.1016/j.spa.2025.104686
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