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Mathematics - Probability Theory and Stochastic Processes | Measure-Valued Branching Markov Processes

Measure-Valued Branching Markov Processes

Li, Zenghu

2011, XI, 350 p.

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  • For the first time a book in this research area
  • Gives treatments of the basic regularities of Dawson-Watanabe superprocesses with general branching mechanisms and spatial motions
  • Studies immigration superprocesses and generalized Ornstein-Uhlenbeck processes
  • Designed as a study text for graduates

Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups.

The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.

Content Level » Graduate

Keywords » 60J80; 60G57; 60J70; 60J85; 60J35; 60J40 - Dawson-Watanabe superprocess - entrance law - generalized Ornstein-Uhlenbeck process - immigration superprocess - skew convolution semigroup

Related subjects » Probability Theory and Stochastic Processes

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