Measure Valued Branching Markov Processes

Author : Zenghu Li
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 54,5 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9783642150043

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Measure-Valued Branching Markov Processes by Zenghu Li Pdf

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.

Author : Evgeniĭ Borisovich Dynkin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 44,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821802694

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An Introduction to Branching Measure-Valued Processes by Evgeniĭ Borisovich Dynkin Pdf

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.

Author : Zenghu Li
Publisher : Springer Nature
Page : 481 pages
File Size : 44,6 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783662669105

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Measure-Valued Branching Markov Processes by Zenghu Li Pdf

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.

Author : Carl Mueller,D. Dawson,Y. Li
Publisher : Unknown
Page : 44 pages
File Size : 50,5 Mb
Release : 1993
Category : Electronic
ISBN : CORNELL:31924067536510

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The Support of Measure Valued Branching Processes in a Random Environment by Carl Mueller,D. Dawson,Y. Li Pdf

Author : Evgeniĭ Borisovich Dynkin,S. E. Kuznetsov,A. V. Skorokhod
Publisher : Unknown
Page : 84 pages
File Size : 54,7 Mb
Release : 1992
Category : Electronic
ISBN : CORNELL:31924063621043

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Branching Measure-valued Processes by Evgeniĭ Borisovich Dynkin,S. E. Kuznetsov,A. V. Skorokhod Pdf

Author : Mark Iosifovich Freĭdlin
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 45,9 Mb
Release : 1994
Category : Mathematics
ISBN : 081763696X

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The Dynkin Festschrift by Mark Iosifovich Freĭdlin Pdf

Eugene B. Dynkin published his first paper, on Markov chain theory, whilst still an undergraduate student at Moscow State University. He went on to make fundamental contributions to the theory of Markov processes and to Lie groups, generating entire schools in these areas.

Author : Krishna B. Athreya,Peter Jagers
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218623

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Classical and Modern Branching Processes by Krishna B. Athreya,Peter Jagers Pdf

This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13-171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes.

Author : Alison Etheridge
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 42,5 Mb
Release : 2000
Category : Random measures
ISBN : 9780821827062

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An Introduction to Superprocesses by Alison Etheridge Pdf

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.

Author : Steven Orey
Publisher : Unknown
Page : 44 pages
File Size : 54,6 Mb
Release : 1959
Category : Markov processes
ISBN : UOM:39015095251131

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Change of Time Scale for Markov Processes by Steven Orey Pdf

Author : Christoph Bandt,Peter Mörters,Martina Zähle
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 50,8 Mb
Release : 2010-01-08
Category : Mathematics
ISBN : 9783034600309

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Fractal Geometry and Stochastics IV by Christoph Bandt,Peter Mörters,Martina Zähle Pdf

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.

Author : Andre Boivin,Javad Mashreghi
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 49,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891735

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Complex Analysis and Potential Theory by Andre Boivin,Javad Mashreghi Pdf

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.

Author : Martin Jacobsen
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 44,9 Mb
Release : 2006-07-27
Category : Mathematics
ISBN : 9780817644635

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Point Process Theory and Applications by Martin Jacobsen Pdf

Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience

Author : Donald Andrew Dawson
Publisher : American Mathematical Soc.
Page : 260 pages
File Size : 55,8 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 0821870440

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Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems by Donald Andrew Dawson Pdf

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.

Author : René Carmona
Publisher : American Mathematical Soc.
Page : 360 pages
File Size : 44,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0821808060

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Stochastic Partial Differential Equations: Six Perspectives by René Carmona Pdf

Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Mark I. Freidlin
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202790

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The Dynkin Festschrift by Mark I. Freidlin Pdf

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.