Conditional Log-Laplace Functionals of Immigration Superprocesses with   Dependent Spatial Motion
  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. 
Zenghu Li, Hao Wang, Jie Xiong