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Ergodic theory for a superprocess over a stochastic flow

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  • Li, Zenghu
  • Xiong, Jie
  • Zhang, Mei

Abstract

We study the long time limiting behavior of the occupation time of the superprocess over a stochastic flow introduced by Skoulakis and Adler (2001) [13]. The ergodic theorems for dimensions d=2 and d>=3 are established. The proofs depend heavily on a characterization of the conditional log-Laplace equation of the occupation time process.

Suggested Citation

  • Li, Zenghu & Xiong, Jie & Zhang, Mei, 2010. "Ergodic theory for a superprocess over a stochastic flow," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1563-1588, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:8:p:1563-1588
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    References listed on IDEAS

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    1. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    2. Donald A. Dawson & Zenghu Li & Hao Wang, 2001. "Superprocesses with Dependent Spatial Motion and General Branching Densities," RePAd Working Paper Series lrsp-TRS346, Département des sciences administratives, UQO.
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