Branching Measure Valued Processes

Author : Evgeniĭ Borisovich Dynkin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 50,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821802694

Get Book

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 Science & Business Media
Page : 356 pages
File Size : 49,6 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9783642150043

Get Book

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 : Zenghu Li
Publisher : Springer Nature
Page : 481 pages
File Size : 46,9 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783662669105

Get Book

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 : Evgeniĭ Borisovich Dynkin,S. E. Kuznetsov,A. V. Skorokhod
Publisher : Unknown
Page : 84 pages
File Size : 41,7 Mb
Release : 1992
Category : Electronic
ISBN : CORNELL:31924063621043

Get Book

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

Author : Jean-Francois Le Gall
Publisher : Birkhäuser
Page : 170 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886833

Get Book

Spatial Branching Processes, Random Snakes and Partial Differential Equations by Jean-Francois Le Gall Pdf

This book introduces several remarkable new probabilistic objects that combine spatial motion with a continuous branching phenomenon and are closely related to certain semilinear partial differential equations (PDE). The Brownian snake approach is used to give a powerful representation of superprocesses and also to investigate connections between superprocesses and PDEs. These are notable because almost every important probabilistic question corresponds to a significant analytic problem.

Author : Edwin Arend Perkins
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 40,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803585

Get Book

On the Martingale Problem for Interactive Measure-Valued Branching Diffusions by Edwin Arend Perkins Pdf

This book develops stochastic integration with respect to ``Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.

Author : Carl Mueller,D. Dawson,Y. Li
Publisher : Unknown
Page : 44 pages
File Size : 47,8 Mb
Release : 1993
Category : Electronic
ISBN : CORNELL:31924067536510

Get Book

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

Author : Edwin Arend Perkins
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 54,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 0821862723

Get Book

On the Martingale Problem for Interactive Measure-valued Branching Diffusions by Edwin Arend Perkins Pdf

This book develops stochastic integration with respect to ''Brownian trees'' and its associated stochastic calculus, with the aim of proving pathwise existence and uniqueness in a stochastic equation driven by a historical Brownian motion. Perkins uses these results and a Girsanov-type theorem to prove that the martingale problem for the historical process associated with a wide class of interactive branching measure-valued diffusions (superprocesses) is well-posed. The resulting measure-valued processes will arise as limits of the empirical measures of branching particle systems in which particles interact through their spatial motions or, to a lesser extent, through their branching rates.

Author : Donald Andrew Dawson,Carleton University. Dept. of Mathematics and Statistics
Publisher : Department of Mathematics and Statistics, Carleton University
Page : 152 pages
File Size : 53,7 Mb
Release : 1982
Category : Branching processes
ISBN : STANFORD:36105032745668

Get Book

Measure-valued Branching Processes by Donald Andrew Dawson,Carleton University. Dept. of Mathematics and Statistics Pdf

Author : Takeyuki Hida,Kimiaki Saito
Publisher : World Scientific
Page : 244 pages
File Size : 47,7 Mb
Release : 2000
Category : Science
ISBN : 9810243170

Get Book

Quantum Information II by Takeyuki Hida,Kimiaki Saito Pdf

http://www.worldscientific.com/worldscibooks/10.1142/4433

Author : Mark I. Freidlin
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202790

Get Book

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.

Author : Alison Etheridge
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 49,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821827062

Get Book

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 : Donald Andrew Dawson,Luis G. Gorostiza,B. Gail Ivanoff
Publisher : American Mathematical Soc.
Page : 492 pages
File Size : 55,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0821810634

Get Book

Stochastic Models by Donald Andrew Dawson,Luis G. Gorostiza,B. Gail Ivanoff Pdf

This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.

Author : Krishna B. Athreya,Peter Jagers
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461218623

Get Book

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 : René Carmona
Publisher : American Mathematical Soc.
Page : 349 pages
File Size : 54,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821821008

Get Book

Stochastic Partial Differential Equations: Six Perspectives by René Carmona Pdf

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. .