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Some quenched and annealed limit theorems for superprocesses in random environments

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  • 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→∞.

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  • 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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    References listed on IDEAS

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    1. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    2. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    3. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 19-35, January.
    4. Bojdecki, T. & Gorostiza, L.G. & Talarczyk, A., 2006. "Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 1-18, January.
    5. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
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