Measure Valued Branching Markov Processes

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Measure Valued Branching Markov Processes
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Author : Zenghu Li
language : en
Publisher: Springer Nature
Release Date : 2023-03-13
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 2023-03-13 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.
An Introduction To Superprocesses
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Author : Alison Etheridge
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
An Introduction To Superprocesses written by Alison Etheridge 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 2000 with Mathematics categories.
Over the past 20 years, the study of superprocesses has expanded into a major industry and can now be regarded as a central theme in modern probability theory. This book is intended as a rapid introduction to the subject, geared toward graduate students and researchers in stochastic analysis. A variety of different approaches to the superprocesses emerged over the last ten years. Yet no one approach superseded any others. In this book, readers are exposed to a number of different ways of thinking about the processes, and each is used to motivate some key results. The emphasis is on why results are true rather than on rigorous proof. Specific results are given, including extensive references to current literature for their general form.
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.
Fractal Geometry And Stochastics Iv
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Author : Christoph Bandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-08
Fractal Geometry And Stochastics Iv written by Christoph Bandt 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 2010-01-08 with Mathematics categories.
Over the last fifteen years fractal geometry has established itself as a substantial mathematical theory in its own right. The interplay between fractal geometry, analysis and stochastics has highly influenced recent developments in mathematical modeling of complicated structures. This process has been forced by problems in these areas related to applications in statistical physics, biomathematics and finance. This book is a collection of survey articles covering many of the most recent developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals. The authors were the keynote speakers at the conference "Fractal Geometry and Stochastics IV" at Greifswald in September 2008.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin 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 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
Stochastic Partial Differential Equations Six Perspectives
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Author : René Carmona
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Stochastic Partial Differential Equations Six Perspectives written by René Carmona 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 1999 with Mathematics categories.
The field of Stochastic Partial Differential Equations (SPDEs) is one of the most dynamically developing areas of mathematics. It lies at the cross section of probability, partial differential equations, population biology, and mathematical physics. The field is especially attractive because of its interdisciplinary nature and the enormous richness of current and potential future applications. This volume is a collection of six important topics in SPDEs presented from the viewpoint of distinguished scientists working in the field and related areas. Emphasized are the genesis and applications of SPDEs as well as mathematical theory and numerical methods. .
Canadian Mathematical Bulletin
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Author :
language : en
Publisher:
Release Date : 1992-03
Canadian Mathematical Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03 with categories.
The Dynkin Festschrift
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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Dynkin Festschrift written by Mark I. Freidlin 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 2012-12-06 with Mathematics categories.
Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.
Ecole D Ete De Probabilites De Saint Flour Xxi 1991
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Author : Donald A. Dawson
language : en
Publisher: Springer
Release Date : 2006-11-14
Ecole D Ete De Probabilites De Saint Flour Xxi 1991 written by Donald A. Dawson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
CONTENTS: D.D. Dawson: Measure-valued Markov Processes.- B. Maisonneuve: Processus de Markov: Naissance, Retournement, Regeneration.- J. Spencer: Nine lectures on Random Graphs.
S Minaire De Probabilit S Xlvi
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Author : Catherine Donati-Martin
language : en
Publisher: Springer
Release Date : 2014-12-29
S Minaire De Probabilit S Xlvi written by Catherine Donati-Martin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-29 with Mathematics categories.
Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.