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| Author | : Krishna B. Athreya |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 301 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642653715 |
Download Branching Processes Book in PDF, ePub and Kindle
The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.
| Author | : Asmussen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1461581559 |
Download Branching Processes Book in PDF, ePub and Kindle
Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.
| Author | : Theodore Edward 1919- Harris |
| Publisher | : Hassell Street Press |
| Total Pages | : 256 |
| Release | : 2021-09-10 |
| Genre | : |
| ISBN | : 9781014914002 |
Download The Theory of Branching Processes Book in PDF, ePub and Kindle
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
| Author | : Patsy Haccou |
| Publisher | : Cambridge University Press |
| Total Pages | : 342 |
| Release | : 2005-05-19 |
| Genre | : Mathematics |
| ISBN | : 9780521832205 |
Download Branching Processes Book in PDF, ePub and Kindle
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
| Author | : Marek Kimmel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 242 |
| Release | : 2002-05-10 |
| Genre | : Mathematics |
| ISBN | : 038795340X |
Download Branching Processes in Biology Book in PDF, ePub and Kindle
Biological examples of branching processes from molecular and cellular biology are introduced in this volume, as well as from the fields of human evolution and medicine. It will interest scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, and others. 54 illustrations.
| Author | : Miguel González Velasco |
| Publisher | : John Wiley & Sons |
| Total Pages | : 232 |
| Release | : 2017-12-27 |
| Genre | : Mathematics |
| ISBN | : 1119484561 |
Download Controlled Branching Processes Book in PDF, ePub and Kindle
The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.
| Author | : Jean-Francois Le Gall |
| Publisher | : Birkhäuser |
| Total Pages | : 170 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034886837 |
Download Spatial Branching Processes, Random Snakes and Partial Differential Equations Book in PDF, ePub and Kindle
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 | : Krishna B. Athreya |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 340 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461218624 |
Download Classical and Modern Branching Processes Book in PDF, ePub and Kindle
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 | : Zenghu Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2010-11-10 |
| Genre | : Mathematics |
| ISBN | : 3642150047 |
Download Measure-Valued Branching Markov Processes Book in PDF, ePub and Kindle
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 | : Inés M. del Puerto |
| Publisher | : Springer |
| Total Pages | : 332 |
| Release | : 2016-09-06 |
| Genre | : Mathematics |
| ISBN | : 3319316419 |
Download Branching Processes and Their Applications Book in PDF, ePub and Kindle
This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.
