Classical And Modern Branching Processes PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Classical And Modern Branching Processes PDF full book. Access full book title Classical And Modern Branching Processes.
| 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 | : 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 | : 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 | : Miguel González Velasco |
| Publisher | : John Wiley & Sons |
| Total Pages | : 240 |
| Release | : 2018-03-13 |
| Genre | : Mathematics |
| ISBN | : 1786302535 |
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 | : 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 | : Theodore Edward Harris |
| Publisher | : Springer |
| Total Pages | : 258 |
| Release | : 1963-11-15 |
| Genre | : Mathematics |
| ISBN | : |
Download The Theory of Branching Processes Book in PDF, ePub and Kindle
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.
| Author | : Miguel González |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2010-03-02 |
| Genre | : Mathematics |
| ISBN | : 3642111564 |
Download Workshop on Branching Processes and Their Applications Book in PDF, ePub and Kindle
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 | : Brigitte Chauvin |
| Publisher | : Birkhäuser |
| Total Pages | : 158 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034890370 |
Download Trees Book in PDF, ePub and Kindle
For the first time, the very different aspects of trees are presented here in one volume. Articles by specialists working in different areas of mathematics cover disordered systems, algorithms, probability, and p-adic analysis. Researchers and graduate students alike will benefit from the clear expositions.
| Author | : Sylvie Meleard |
| Publisher | : Springer |
| Total Pages | : 111 |
| Release | : 2015-09-03 |
| Genre | : Mathematics |
| ISBN | : 3319217119 |
Download Stochastic Models for Structured Populations Book in PDF, ePub and Kindle
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
| Author | : Étienne Pardoux |
| Publisher | : Springer |
| Total Pages | : 129 |
| Release | : 2016-06-17 |
| Genre | : Mathematics |
| ISBN | : 3319303287 |
Download Probabilistic Models of Population Evolution Book in PDF, ePub and Kindle
This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications. Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, stochastic partial differential equations, and probabilistic models in evolutionary biology and population genetics. He obtained his PhD in 1975 at University of Paris-Sud.
