Critical Age Dependent Branching Processes

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Critical Age Dependent Branching Processes

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Author : Martin Ivan Goldstein
language : en
Publisher:
Release Date : 1969

Critical Age Dependent Branching Processes written by Martin Ivan Goldstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Branching processes categories.

Limit Probabilities For Critical Age Dependent Branching Processes With Immigration

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Author : STANFORD UNIV CALIF DEPT OF STATISTICS.
language : en
Publisher:
Release Date : 1979

Limit Probabilities For Critical Age Dependent Branching Processes With Immigration written by STANFORD UNIV CALIF DEPT OF STATISTICS. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.

Let Z sub O(t), N sub O (t) denote, respectively, the number of cells alive at t and the total progeny born by t in a process with a random number of new cells introduced at renewal epochs, each new cell initiating a critical age-dependent branching process. As t approaches infinity, the forms of P(Z sub O (t) = k) and P(N sub O (t) = k) are obtained for k = 1,2, ... and k = 0,1,2, ..., respectively. A multi-dimensional version and extension are indicated.

Total Progency In A Critical Age Dependent Branching Process With Immigration

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Author : Howard Weiner
language : en
Publisher:
Release Date : 1976

Total Progency In A Critical Age Dependent Branching Process With Immigration written by Howard Weiner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.

Let Z(t) = total number of cells born by t to critical age-dependent branching processes initiated by immigration at renewal epochs, with a random number of new cells introduced at each epoch, and where the mean cell lifetime is unequal to that of the mean time between immigration epochs. By extending a result for the discrete-time case of Pakes, and using approximation techniques and a rate of convergence result for a generalized law of large numbers, it is shown that, using second moments that the limit of E as t approaches infinity for exp( - theta t square z(t)) exists, and is explicitly given.

Branching Processes And Their Applications

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Author : Inés M. del Puerto
language : en
Publisher: Springer
Release Date : 2016-09-06

Branching Processes And Their Applications written by Inés M. del Puerto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Mathematics categories.

This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics. The topics covered can broadly be classified into the following areas: 1. Coalescent Branching Processes 2. Branching Random Walks 3. Population Growth Models in Varying and Random Environments 4. Size/Density/Resource-Dependent Branching Models 5. Age-Dependent Branching Models 6. Special Branching Models 7. Applications in Epidemiology 8. Applications in Biology and Genetics Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.

Growth Of The Maximum In A Critical Age Dependent Branching Process

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Author : STANFORD UNIV CA DEPT OF STATISTICS.
language : en
Publisher:
Release Date : 1981

Growth Of The Maximum In A Critical Age Dependent Branching Process written by STANFORD UNIV CA DEPT OF STATISTICS. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.

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.

Conditioned Limit Laws In Critical Age Dependent Branching Processes And Some Associated Diffusions

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Author : Warren W. Esty
language : en
Publisher:
Release Date : 1973

Conditioned Limit Laws In Critical Age Dependent Branching Processes And Some Associated Diffusions written by Warren W. Esty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.

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.

Random Sums And Branching Stochastic Processes

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Author : Ibrahim Rahimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Random Sums And Branching Stochastic Processes written by Ibrahim Rahimov 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 aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.