An Introduction To Branching Measure Valued Processes
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An Introduction To Branching Measure Valued Processes
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Author : Evgeniĭ Borisovich Dynkin
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
An Introduction To Branching Measure Valued Processes written by Evgeniĭ Borisovich Dynkin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
For about half a century, two classes of stochastic processes---Gaussian processes and processes with independent increments---have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class---branching measure-valued (BMV) processes---has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.
Measure Valued Branching Markov Processes
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Author : Zenghu Li
language : en
Publisher:
Release Date : 2022
Measure Valued Branching Markov Processes written by Zenghu Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
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 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. 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.
The Support Of Measure Valued Branching Processes In A Random Environment
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Author : Carl Mueller
language : en
Publisher:
Release Date : 1993
The Support Of Measure Valued Branching Processes In A Random Environment written by Carl Mueller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Measure Valued Branching Processes
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Author : Donald Andrew Dawson
language : en
Publisher: Department of Mathematics and Statistics, Carleton University
Release Date : 1982
Measure Valued Branching Processes written by Donald Andrew Dawson and has been published by Department of Mathematics and Statistics, Carleton University this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Branching processes categories.
Measure Valued Branching Markov Processes
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Author : Zenghu Li
language : en
Publisher: Springer Nature
Release Date : 2023-04-14
Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-14 with Mathematics categories.
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 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. 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.
Measure Valued Branching Processes A Collection Of Four Papers
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Author : D. A. Dawson
language : en
Publisher:
Release Date : 1982
Measure Valued Branching Processes A Collection Of Four Papers written by D. A. Dawson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Measure Valued Branching Markov Processes
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Author : Zenghu Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10
Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
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.
Two Papers On A Class Of Branching Measure Valued Processes
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Author : Guillaume Leduc
language : en
Publisher:
Release Date : 1995
Two Papers On A Class Of Branching Measure Valued Processes written by Guillaume Leduc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Branching processes categories.
Measure Valued Processes Stochastic Partial Differential Equations And Interacting Systems
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Author : Donald Andrew Dawson
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-01-01
Measure Valued Processes Stochastic Partial Differential Equations And Interacting Systems written by Donald Andrew Dawson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
The papers in this collection explore the connections between the rapidly developing fields of measure-valued processes, stochastic partial differential equations, and interacting particle systems, each of which has undergone profound development in recent years. Bringing together ideas and tools arising from these different sources, the papers include contributions to major directions of research in these fields, explore the interface between them, and describe newly developing research problems and methodologies. Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these processes are described, including branching in catalytic media, branching with change of mass, and multilevel branching. Sample path and spatial clumping properties of superprocesses are also studied. The papers on Fleming-Viot processes arising in population genetics include discussions of the role of genealogical structures and the application of the Dirichlet form methodology. Several papers are devoted to particle systems studied in statistical physics and to stochastic partial differential equations which arise as hydrodynamic limits of such systems. With overview articles on some of the important new developments in these areas, this book would be an ideal source for an advanced graduate course on superprocesses.
Branching Measure Valued Processes
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Author : Evgeniĭ Borisovich Dynkin
language : en
Publisher:
Release Date : 1992
Branching Measure Valued Processes written by Evgeniĭ Borisovich Dynkin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.