The Genealogy of Branching Processes
Author | : Neil Michael O'Connell |
Publisher | : |
Total Pages | : 260 |
Release | : 1993 |
Genre | : |
ISBN | : |
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Author | : Neil Michael O'Connell |
Publisher | : |
Total Pages | : 260 |
Release | : 1993 |
Genre | : |
ISBN | : |
Author | : Pascal Vogt |
Publisher | : |
Total Pages | : |
Release | : 2001 |
Genre | : |
ISBN | : |
Author | : Asmussen |
Publisher | : Springer Science & Business Media |
Total Pages | : 468 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1461581559 |
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 | : Krishna B. Athreya |
Publisher | : Springer Science & Business Media |
Total Pages | : 301 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642653715 |
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 | : Jean-Francois Le Gall |
Publisher | : Birkhäuser |
Total Pages | : 170 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034886837 |
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 | : Ziad Taib |
Publisher | : Springer |
Total Pages | : 112 |
Release | : 1992-07-08 |
Genre | : Mathematics |
ISBN | : 9783540555292 |
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.
Author | : |
Publisher | : |
Total Pages | : 13 |
Release | : 2006 |
Genre | : |
ISBN | : |
Author | : Miguel González |
Publisher | : Springer Science & Business Media |
Total Pages | : 304 |
Release | : 2010-03-02 |
Genre | : Mathematics |
ISBN | : 3642111564 |
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.
Author | : C.C. Heyde |
Publisher | : Springer Science & Business Media |
Total Pages | : 189 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461225582 |
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.
Author | : Lea Popovic |
Publisher | : Ann Arbor, Mich. : University Microfilms International |
Total Pages | : 156 |
Release | : 2003 |
Genre | : |
ISBN | : |