BRANCHING PARTICLE-SYSTEMS AND SUPERPROCESSES

• 成果类型: Article
• 署名作者: DYNKIN, EB
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990339
• 发表日期: 1991
• 页码: 1157-1194
• 关键词: super-brownian motion; additive-functionals; CONSTRUCTION

摘要

We start from a model of a branching particle system with immigration and with death rate and branching mechanism depending on time and location. Then we consider a limit case when the mass of particles and their life times are small and their density is high. This way, we construct a measure-valued process X(t) which we call a superprocess. Replacing the underlying Markov process xi-t by the corresponding historical process xi less-than-or-equal-to t, we construct a measure-valued process M(t) in functional spaces which we call a historical superprocess. The moment functions for superprocesses are evaluated. Linear positive additive functionals are studied. They are used to construct a continuous analog of a random tree obtained by stopping every particle at a time depending on its path (say, at the first exit time from a domain). A related special Markov property for superprocesses is proved which is useful for applications to certain nonlinear partial differential equations. The concluding section is devoted to a survey of the literature, and the terminology on Markov processes used in the paper is explained in the Appendix.