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The Theory of Branching Processes

Release on 19631963 by Theodore Edward Harris
The Theory of Branching Processes

Author: Theodore Edward Harris

Publisher: Springer

ISBN: 3642518664

Category: Mathematics

Page: 0

View: 283

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.
Mathematics
The Theory of Branching Processes
Language: en
Pages: 0

The Theory of Branching Processes

Authors: Theodore Edward Harris
Categories: Mathematics
Type: BOOK - Published: 1963 - Publisher: Springer

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
Spatial Branching Processes, Random Snakes and Partial Differential Equations
Language: en
Pages: 163

Spatial Branching Processes, Random Snakes and Partial Differential Equations

Authors: Jean-Francois Le Gall
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

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.
Branching Processes
Language: en
Pages: 342

Branching Processes

Authors: Patsy Haccou, Patricia Haccou, Peter Jagers, Vladimir A. Vatutin, Vladimir Vatutin
Categories: Mathematics
Type: BOOK - Published: 2005-05-19 - Publisher: Cambridge University Press

This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Branching Processes
Language: en
Pages: 461

Branching Processes

Authors: Asmussen, Hering
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

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
Branching Processes
Language: en
Pages: 288

Branching Processes

Authors: Krishna B. Athreya, Peter E. Ney
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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

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