WIAS Preprint No. 900, (2004)

Conditional log-Laplace functionals of immigration superprocesses with dependent spatial motion



Authors

  • Li, Zenghu
  • Wang, Hao
  • Xiong, Jie

2010 Mathematics Subject Classification

  • 60J80 60G57 60J35

Keywords

  • branching particle system, superprocess, dependent spatial motion, immigration process, non-linear SPDE, conditional log-Laplace functional

Abstract

A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A representation of its conditional log-Laplace functionals is established, which gives the uniqueness of the solution and hence its Markov property. Some properties of the superprocess including an ergodic theorem are also obtained.

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