Measure-Valued Branching Markov Processes - Brossura

Zenghu Li, Li

 
9783662669112: Measure-Valued Branching Markov Processes
Brossura
ISBN 10: 3662669110 ISBN 13: 9783662669112
Casa editrice: Springer, 2023

Sinossi

This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein-Uhlenbeck type processes.

Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson-Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skewconvolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses.

This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.


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Editore
Springer
Data di pubblicazione
2023
Lingua
Inglese
ISBN 10 
3662669110
ISBN 13 
9783662669112
Rilegatura
Copertina flessibile
Numero di pagine
492
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Hamburg
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Altre edizioni note dello stesso titolo

9783642150036: Measure-Valued Branching Markov Processes

Edizione in evidenza

ISBN 10:  3642150039 ISBN 13:  9783642150036
Casa editrice: Springer Nature, 2010
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