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Measure Valued Branching Processes
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Book Synopsis Measure-Valued Branching Markov Processes by : Zenghu Li
Download or read book Measure-Valued Branching Markov Processes written by Zenghu Li and published by Springer Science & Business Media. This book was released on 2010-11-10 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Measure-Valued Branching Markov Processes by : Zenghu Li
Download or read book Measure-Valued Branching Markov Processes written by Zenghu Li and published by Springer Nature. This book was released on 2023-04-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spatial Branching Processes, Random Snakes and Partial Differential Equations by : Jean-Francois Le Gall
Download or read book Spatial Branching Processes, Random Snakes and Partial Differential Equations written by Jean-Francois Le Gall and published by Birkhäuser. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Branching Measure-Valued Processes by : Evgeniĭ Borisovich Dynkin
Download or read book An Introduction to Branching Measure-Valued Processes written by Evgeniĭ Borisovich Dynkin and published by American Mathematical Soc.. This book was released on 1994 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :Donald Andrew Dawson Publisher :Department of Mathematics and Statistics, Carleton University ISBN 13 : Total Pages :152 pages Book Rating :4.F/5 ( download)
Book Synopsis Measure-valued Branching Processes by : Donald Andrew Dawson
Download or read book Measure-valued Branching Processes written by Donald Andrew Dawson and published by Department of Mathematics and Statistics, Carleton University. This book was released on 1982 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Support of Measure Valued Branching Processes in a Random Environment by : Carl Mueller
Download or read book The Support of Measure Valued Branching Processes in a Random Environment written by Carl Mueller and published by . This book was released on 1993 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classical and Modern Branching Processes by : Krishna B. Athreya
Download or read book Classical and Modern Branching Processes written by Krishna B. Athreya and published by Springer. This book was released on 1997 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis On the Martingale Problem for Interactive Measure-Valued Branching Diffusions by : Edwin Arend Perkins
Download or read book On the Martingale Problem for Interactive Measure-Valued Branching Diffusions written by Edwin Arend Perkins and published by American Mathematical Soc.. This book was released on 1995 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Partial Differential Equations by : Sergey V. Lototsky
Download or read book Stochastic Partial Differential Equations written by Sergey V. Lototsky and published by Springer. This book was released on 2017-07-06 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.
Book Synopsis An Introduction to Superprocesses by : Alison Etheridge
Download or read book An Introduction to Superprocesses written by Alison Etheridge and published by American Mathematical Soc.. This book was released on 2000 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Models by : Donald Andrew Dawson
Download or read book Stochastic Models written by Donald Andrew Dawson and published by American Mathematical Soc.. This book was released on 2000 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical and Modern Branching Processes by : Krishna B. Athreya
Download or read book Classical and Modern Branching Processes written by Krishna B. Athreya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Information II by : Takeyuki Hida
Download or read book Quantum Information II written by Takeyuki Hida and published by World Scientific. This book was released on 2000 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: http://www.worldscientific.com/worldscibooks/10.1142/4433
Book Synopsis Fractal Geometry and Stochastics IV by : Christoph Bandt
Download or read book Fractal Geometry and Stochastics IV written by Christoph Bandt and published by Springer Science & Business Media. This book was released on 2010-01-08 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Partial Differential Equations: Six Perspectives by : René Carmona
Download or read book Stochastic Partial Differential Equations: Six Perspectives written by René Carmona and published by American Mathematical Soc.. This book was released on 1999 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. .
Book Synopsis Historical Processes by : Donald Andrew Dawson
Download or read book Historical Processes written by Donald Andrew Dawson and published by American Mathematical Soc.. This book was released on 1991 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The historical process is constructed to be a superprocess associated with a general motion process and branching mechanism, which is enriched so as to contain information on genealogy. In other words, it is a Markov process taking values in the space of measures on the set of possible histories. Using the canonical representation for the infinitely divisible random measures which describe the process at fixed times, the authors obtain analytical and probabilistic representations for the associated Palm measures. They employ these representations to obtain results on the modulus of continuity and equilibirium structure for a class of superprocesses in Rd and to establish that super-Brownian motion in dimensions d 53 has constant density with respect to the appropriate Hausdorff measure.
Book Synopsis Ecole d'Ete de Probabilites de Saint-Flour XXI - 1991 by : Donald A. Dawson
Download or read book Ecole d'Ete de Probabilites de Saint-Flour XXI - 1991 written by Donald A. Dawson and published by Springer. This book was released on 2006-11-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: CONTENTS: D.D. Dawson: Measure-valued Markov Processes.- B. Maisonneuve: Processus de Markov: Naissance, Retournement, Regeneration.- J. Spencer: Nine lectures on Random Graphs.
