Conditional log-Laplace functionals of immigration superprocesses with dependent spatial motion
- Li, Zenghu
- Wang, Hao
- Xiong, Jie
2010 Mathematics Subject Classification
- 60J80 60G57 60J35
- branching particle system, superprocess, dependent spatial motion, immigration process, non-linear SPDE, conditional log-Laplace functional
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.