Format:
Online-Ressource (XX, 296p, digital)
ISBN:
9783642111563
Series Statement:
Lecture Notes in Statistics 197
Content:
Population Growth Models in Random and Varying Environments -- A refinement of limit theorems for the critical branching processes in random environment -- Branching processes in stationary random environment: The extinction problem revisited -- Environmental versus demographic stochasticity in population growth -- Stationary distributions of the alternating branching processes -- Special Branching Processes -- Approximations in population-dependent branching processes -- Extension of the problem of extinction on Galton–Watson family trees -- Limit theorems for critical randomly indexed branching processes -- Renewal measure density for distributions with regularly varying tails of order a ? ? (0,½] -- Limit Theorems and Statistics -- Approximation of a sum of martingale differences generated by a bootstrap branching process -- Critical branching processes with immigration -- Weighted conditional least squares estimation in controlled multitype branching processes -- Applications in Cell Kinetics and Genetics -- Branching processes in cell proliferation kinetics -- Griffiths–Pakes branching process as a model for evolution of Alu elements -- Parametric inference for Y-linked gene branching models: Expectation-maximization method -- Applications in Epidemiology -- Applications of branching processes to the final size of SIR epidemics -- A branching process approach for the propagation of the Bovine Spongiform Encephalopathy in Great-Britain -- Time to extinction of infectious diseases through age-dependent branching models -- Time to extinction in a two-host interaction model for the macroparasite Echinococcus granulosus -- Two-sex Branching Models -- Bisexual branching processes with immigration depending on the number of females and males -- Two-sex branching process literature.
Content:
This volume contains papers presented at the Workshop on Branching Processes and Their Applications (WBPA09). These papers deal with theoretical and practical aspects of branching process theory, showing it to be an area of active and interesting research. They clearly indicate the vitality of the theoretical research on this topic, as well as the importance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Cell Kinetics, Genetics, and, of course, Population Dynamics. The topics covered by the papers have been classified into the following areas: Population Growth Models in Random and Varying Environments Special Branching Processes Limit Theorems and Statistics Applications in Cell Kinetics and Genetics Applications in Epidemiology Two-Sex Branching Models This book represents a valuable reference on the contemporary branching processes theory, presenting also many open problems which will lead to future research.
Note:
Includes bibliographical references and index
,
Foreword; Preface; Contents; Contributors; Part I Population Growth Models in Random and Varying Environments; 1 A refinement of limit theorems for the critical branching processes in random environment; Vladimir Vatutin; 1.1 Introduction and main results; 1.2 Branching in conditioned environment; 1.3 Proof of Theorems 1.1 and 1.2; References; 2 Branching processes in stationary random environment: The extinction problem revisited; Gerold Alsmeyer; 2.1 Introduction; 2.2 Classical results revisited; 2.3 Main result and a counterexample; 2.4 Some useful facts from Palm-duality theory
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2.5 ProofsReferences; 3 Environmental versus demographic stochasticity in population growth; Carlos A. Braumann; 3.1 Introduction; 3.2 Density-independent models and their local behavior; 3.3 Density-independent models and extinction; 3.4 Density-dependent models for environmental stochasticity; 3.5 Conclusions; References; 4 Stationary distributions of the alternating branching processes; Penka Mayster; 4.1 Introduction; 4.2 Alternating branching process; 4.3 Alternating branching process with explicit immigration; 4.4 Reproduction by n cycles; 4.5 Criticality
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4.6 Stationary distribution in random environment4.7 Unconditional probability generating functions; 4.8 Feed-back control; References; Part II Special Branching Processes; 5 Approximations in population-dependent branching processes; Fima C. Klebaner; 5.1 Introduction and a motivating example; 5.2 A Representation of the process and its re-scaled version; 5.2.1 Re-scaled process: Dynamics plus small noise; 5.2.2 Dynamics without noise in binary splitting; 5.3 Time to extinction; 5.4 The size of the population after a long time providedit has survived; 5.5 Case of small initial population
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5.5.1 Probability of becoming large and time for it to happen5.6 Behaviour before extinction; References; 6 Extension of the problem of extinction on Galton--Watson family trees; George P. Yanev; 6.1 Introduction; 6.2 Critical phenomenon; 6.3 Distribution of the number of complete and disjoint subtrees, rooted at the ancestor; 6.4 Ratio of expected values of Zns provided infinite subtrees exist; 6.6 Poisson offspring distribution; 6.7 One-or-many offspring distribution; 6.8 Concluding remarks; References; 7 Limit theorems for critical randomly indexed branching processes
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Kosto V. Mitov, Georgi K. Mitov and Nikolay M. Yanev7.1 Introduction; 7.2 A conditional limit theorem for random time change; 7.3 Renewal processes; 7.4 BGW branching processes starting with random number of particles; 7.5 Limit theorems for the process Y(t); 7.6 Concluding remarks; References; 8 Renewal measure density for distributions with regularly varying tails of order (0,1/2]; Valentin Topchii; 8.1 Introduction; 8.2 Effects of attraction to a stable law; 8.3 Asymptotics of renewal function density; References; Part III Limit Theorems and Statistics
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9 Approximation of a sum of martingale differences generated by a bootstrap branching process
Additional Edition:
ISBN 9783642111549
Additional Edition:
Buchausg. u.d.T. Workshop on Branching Processes and Their Applications (2009 : Badajoz) Workshop on Branching Processes and Their Applications Berlin : Springer, 2010 ISBN 9783642111549
Language:
English
Subjects:
Mathematics
Keywords:
Verzweigungsprozess
;
Verzweigungsprozess
;
Konferenzschrift
DOI:
10.1007/978-3-642-11156-3
URL:
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URL:
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