Branching Processes
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Branching Processes
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Author : K. B. Athreya
language : en
Publisher: Courier Corporation
Release Date : 2004-03-19
Branching Processes written by K. B. Athreya and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-19 with Mathematics categories.
A unified treatment of the limit theory of branching processes, this volume focuses on basics and is appropriate for graduate and advanced undergraduate students. The authors cover basic Galton-Watson process, potential theory, one dimensional continuous time Markov branching processes, age-dependent processes, multi-type branching processes, and special processes. Exercises. 1972 edition.
Branching Processes
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Author : Patsy Haccou
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-19
Branching Processes written by Patsy Haccou and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Mathematics categories.
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
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.
The Theory Of Branching Processes
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Author : Theodore Edward Harris
language : en
Publisher: Springer
Release Date : 1963-11-15
The Theory Of Branching Processes written by Theodore Edward Harris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963-11-15 with Mathematics categories.
It was about ninety years ago that GALTON and WATSON, in treating the problem of the extinction of family names, showed how probability theory could be applied to study the effects of chance on the development of families or populations. They formulated a mathematical model, which was neglected for many years after their original work, but was studied again in isolated papers in the twenties and thirties of this century. During the past fifteen or twenty years, the model and its general izations have been treated extensively, for their mathematical interest and as a theoretical basis for studies of populations of such objects as genes, neutrons, or cosmic rays. The generalizations of the GaIton Wa,tson model to be studied in this book can appropriately be called branching processes; the term has become common since its use in a more restricted sense in a paper by KOLMOGOROV and DMITRIEV in 1947 (see Chapter II). We may think of a branching process as a mathematical representation of the development of a population whose members reproduce and die, subject to laws of chance. The objects may be of different types, depending on their age, energy, position, or other factors. However, they must not interfere with one another. This assump tion, which unifies the mathematical theory, seems justified for some populations of physical particles such as neutrons or cosmic rays, but only under very restricted circumstances for biological populations.
Branching Processes With Biological Applications
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Author : Peter Jagers
language : en
Publisher: Wiley-Interscience
Release Date : 1975
Branching Processes With Biological Applications written by Peter Jagers and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Science categories.
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.
Multitype Branching Processes
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Author : Charles J. Mode
language : en
Publisher:
Release Date : 1971
Multitype Branching Processes written by Charles J. Mode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Branching Processes In Biology
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Author : Marek Kimmel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-26
Branching Processes In Biology written by Marek Kimmel 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 2006-05-26 with Mathematics categories.
In this book biological examples of Branching Processes are introduced from molecular and cellular biology as well as from the fields of human evolution and medicine and discussed in the context of the relevant mathematics, providing a useful introduction on how the modelling can be done and for what types of problems branching processes can be useful. As an aid to understanding specific examples, two introductory chapters provide background material in mathematics and biology. This book will interest scientists who work in quantitative modelling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, and cell and molecular biologists and bioinformaticians. The authors of this monograph are a mathematician and a cell biologist who have collaborated in the field of Branching Processes for more than a decade.
Discrete Time Branching Processes In Random Environment
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Author : Götz Kersting
language : en
Publisher: John Wiley & Sons
Release Date : 2017-11-01
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 2017-11-01 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.