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Measure-Valued Branching Markov Processes (Probability Theory and Stochastic Modelling, 103) Ed 2 free ebook download

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Mathematics

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Author(s):	Zenghu Li

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3662669099
Pages:	490	OCR:		Quality:		ISBN13:
Uploader:	gestalt	Upload Date:	7/15/2023 9:34:08 AM

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This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and OrnsteinUhlenbeck 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 DawsonWatanabe 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 skew convolution 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.

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Tags: Branching Markov Measure-Valued Modelling Probability Processes Stochastic Theory

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Measure-Valued Branching Markov Processes (Probability Theory and Stochastic Modelling, 103) Ed 2 free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics