Limiting Distributions For Critical Multitype Branching Processes
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Limiting Distributions For Critical Multitype Branching Processes
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Author : T. W. Mullikin
language : en
Publisher:
Release Date : 1961
Limiting Distributions For Critical Multitype Branching Processes written by T. W. Mullikin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Branching processes categories.
Limiting Distributions For Critical Multitype Branching Processes With Discrete Time
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Author : T. W. Mullikin
language : en
Publisher:
Release Date : 1961
Limiting Distributions For Critical Multitype Branching Processes With Discrete Time written by T. W. Mullikin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Branching processes categories.
The theory of branching processes treats the multiplication of objects subject to laws of chance. It has been applied to such phenomena as bacterial fission, cosmic ray showers, and neutron chain reactions. This report describes the probability law governing the descendants of a single object after many generations, if on the average an object has just one surviving child (in the language of reactors, this is the critical case). These results could be useful in the study of controlled nuclear reactions. (Author).
Branching Processes
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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Branching Processes written by Krishna B. Athreya 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.
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.
Discrete Time Branching Processes In Random Environment
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Author : Götz Kersting
language : en
Publisher: John Wiley & Sons
Release Date : 2017-11-29
Discrete Time Branching Processes In Random Environment written by Götz Kersting and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-29 with Mathematics categories.
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Branching Processes
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Author : Asmussen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Branching Processes written by Asmussen 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 2013-06-29 with Mathematics categories.
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.
Branching Processes
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Author : C.C. Heyde
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Branching Processes written by C.C. Heyde 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.
This volume presents the edited proceedings of the First World Congress on Branching Processes. The contributions present new research and surveys of the current research activity in this field. As a result, all those undertaking research in the subject will find this a timely and high-quality volume to have on their shelves.
Branching Processes And Neutral Evolution
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Author : Ziad Taib
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Branching Processes And Neutral Evolution written by Ziad Taib 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 2013-03-09 with Mathematics categories.
The Galton-Watson branching process has its roots in the problem of extinction of family names which was given a precise formulation by F. Galton as problem 4001 in the Educational Times (17, 1873). In 1875, an attempt to solve this problem was made by H. W. Watson but as it turned out, his conclusion was incorrect. Half a century later, R. A. Fisher made use of the Galton-Watson process to determine the extinction probability of the progeny of a mutant gene. However, it was J. B. S. Haldane who finally gave the first sketch of the correct conclusion. J. B. S. Haldane also predicted that mathematical genetics might some day develop into a "respectable branch of applied mathematics" (quoted in M. Kimura & T. Ohta, Theoretical Aspects of Population Genetics. Princeton, 1971). Since the time of Fisher and Haldane, the two fields of branching processes and mathematical genetics have attained a high degree of sophistication but in different directions. This monograph is a first attempt to apply the current state of knowledge concerning single-type branching processes to a particular area of mathematical genetics: neutral evolution. The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. Following the advice of an anonymous referee, I have enlarged my original version of the introduction (Chapter Zero) in order to make it accessible to a larger audience. G6teborg, Sweden, November 1991.
Workshop On Branching Processes And Their Applications
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Author : Miguel González
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-02
Workshop On Branching Processes And Their Applications written by Miguel González 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 2010-03-02 with Mathematics categories.
One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.
The Age Dependent Branching Process With Variable Lifetime Distribution
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Author : Robert Alan Fildes
language : en
Publisher:
Release Date : 1971
The Age Dependent Branching Process With Variable Lifetime Distribution written by Robert Alan Fildes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
Electron Photon Cascades
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Author : Vladimir V. Uchaikin
language : en
Publisher: Springer Nature
Release Date : 2024-07-29
Electron Photon Cascades written by Vladimir V. Uchaikin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-29 with Science categories.
This book demonstrates the practical application of an alternative approach to current problems in high-energy astrophysics. In high-energy astrophysical processes, single collisions are accompanied by the appearance of many secondary particles with different properties. To describe the infinitesimal evolution of such a system at a measurement instant, as is commonly done when deriving the kinetic equation for the system with conserved number of particles, one must know either its prehistory or the infinite family of many-particle distributions. An alternative to this approach is to use an adjoint (in the sense of Lagrange) mathematical formalism, where the independent active variable is the phase position of a primary particle generating the cascade, and the dependent variable has the form of a functional of the cascade as a whole, interpreted as the reading of some not necessarily linear (additive) detector. This approach is characterized by mathematical efficiency: no matter how many particles are formed in a cascade, the active argument of the desired functional always remains one particle. The second advantage is its generality: the formalization of the readings of the detector, which performs real measurements through the functionality of a random implementation of the cascade, allows it to be applied to a wide range of actually used devices and installations. Readers will be able to master the fundamentals of particle astrophysics in the context of the latest developments in the field. It will benefit graduate students and established researchers alike, equipping them with the knowledge and tools necessary to design and interpret their own experiments and, ultimately, to address a number of questions about the nature and origin of cosmic particles that have arisen in recent research.