Branching Processes. Krishna B. Athreya , Peter E. 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.
|Published (Last):||15 May 2009|
|PDF File Size:||19.74 Mb|
|ePub File Size:||11.28 Mb|
|Price:||Free* [*Free Regsitration Required]|
Branching Processes. Krishna B. Athreya , Peter E. 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, 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.
An Important Example. Extinction Probability. Conditioned Limit Laws. AgeDependent Processes 1 Introduction. Existence and Uniqueness. Asymptotic Behavior of Fst in the Critical Case. The Malthusian Case. SubExponential Case. Finer Limit Theorems. Geometric Convergence of fs in the Noncritical Cases. Further Ramifications. Second Order Properties of Z m. More on Conditioning Limiting Diffusions. Complements and Problems I.
Potential Theory 1 Introduction. Existence Uniqueness and Representation. Asymptotic Properties of Stationary Measures. Green Function Behavior. Harmonic Functions. The SpaceTime Boundary. Complements and Problems II. Generating Functions. Extinction Probability and Moments. Binary Fission Birth and Death Process.
More on Generating Functions. Second Order Properties. Constructions Related to Poisson Processes. The Embeddability Problem. Complements and Problems III. Limit Theorems for the Supercritical Case. Complements and Problems IV. Moments and the Frobenius Theorem. Extinction Probability and Transience. Limit Theorems for the Critical Case. The Supercritical Case and Geometric Growth.
Linear Functionals of Supercritical Processes. The Multitype AgeDependent Process. Complements and Problems V. Special Processes. Cascades Distributions of Generations. Branching Diffusions. Martingale Methods. Branching Processes with Random Environments. Continuous State Branching Processes. Complements and Problems VI. List of Symbols. Author Index. Subject Index. Ney , P. Branching Processes Krishna B. Ratio Theorems. Renewal Theory. The QProcess. Limit Theorems.
Split Times. Branching Processes K.
It seems that you're in Germany. We have a dedicated site for Germany. Authors: Athreya , Krishna B. The purpose of this book is to give a unified treatment of the limit theory of branching processes.