Branching Processes. (= Die Grundlehren der mathematischen Wissenschaften - Band 196). - used book

EAN (ISBN-13): 9783540057901
ISBN (ISBN-10): 3540057900
Hardcover
Publishing year: 1972
Publisher: Springer-Vlg., Berlin

Book in our database since 2008-10-03T10:12:10-04:00 (New York)
Detail page last modified on 2023-06-05T09:32:28-04:00 (New York)
ISBN/EAN: 9783540057901

ISBN - alternate spelling:
3-540-05790-0, 978-3-540-05790-1
Alternate spelling and related search-keywords:
Book author: athreya, ney
Book title: die grundlehren der mathematischen wissenschaften, der process, branching processes, mathematischen wissenschaften einzeldarstellungen

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Information from Publisher

Author: Krishna B. Athreya; Peter E. Ney
Title: Grundlehren der mathematischen Wissenschaften; Branching Processes - A Series of Comprehensive Studies in Mathematics
Publisher: Springer; Springer Berlin
288 Pages
Publishing year: 1972-11-29
Berlin; Heidelberg; DE
Weight: 0,600 kg
Language: English
85,55 € (DE)
87,95 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Sonstiges; Angewandte Mathematik; Verstehen; Poisson process; Galton-Watson process; Sharp; construction; renewal theory; proof; branching random walk; Martingale; random walk; techniques; probability; time; Verzweigungsprozess; extinction probability; Branching process; C; Applications of Mathematics; Mathematics and Statistics; BC; EA

I. The Galton-Watson Process.- A. Preliminaries.- 1. The Basic Setting.- 2. Moments.- 3. Elementary Properties of Generating Functions.- 4. An Important Example.- 5. Extinction Probability.- B. A First Look at Limit Theorems.- 6. Motivating Remarks.- 7. Ratio Theorems.- 8. Conditioned Limit Laws.- 9. The Exponential Limit Law for the Critical Process.- C. Finer Limit Theorems.- 10. Strong Convergence in the Supercritical Case.- 11. Geometric Convergence of fn(s) in the Noncritical Cases.- D. Further Ramifications.- 12. Decomposition of the Supercritical Branching Process.- 13. Second Order Properties of Zn/mn.- 14. The Q-Process.- 15. More on Conditioning; Limiting Diffusions.- Complements and Problems I.- II. Potential Theory.- 1. Introduction.- 2. Stationary Measures: Existence, Uniqueness, and Representation.- 3. The Local Limit Theorem for the Critical Case.- 4. The Local Limit Theorem for the Supercritical Case.- 5. Further Properties of W; A Sharp Global Limit Law; Positivity of the Density.- 6. Asymptotic Properties of Stationary Measures.- 7. Green Function Behavior.- 8. Harmonic Functions.- 9. The Space-Time Boundary.- Complements and Problems II.- III. One Dimensional Continuous Time Markov Branching Processes.- 1. Definition.- 2. Construction.- 3. Generating Functions.- 4. Extinction Probability and Moments.- 5. Examples: Binary Fission, Birth and Death Process.- 6. The Embedded Galton-Watson Process and Applications to Moments.- 7. Limit Theorems.- 8. More on Generating Functions.- 9. Split Times.- 10. Second Order Properties.- 11. Constructions Related to Poisson Processes.- 12. The Embeddability Problem.- Complements and Problems III.- IV. Age-Dependent Processes.- 1. Introduction.- 2. Existence and Uniqueness.- 3. Comparison with Galton-Watson Process; Embedded Generation Process; Extinction Probability.- 4. Renewal Theory.- 5. Moments.- 6. Asymptotic Behavior of F(s, t) in the Critical Case.- 7. Asymptotic Behavior of F(s, t) when m?1: The Malthusian Case.- 8. Asymptotic Behavior of F(s, t) when m?1: Sub-Exponential Case.- 9. The Exponential Limit Law in the Critical Case.- 10. The Limit Law for the Subcritical Age-Dependent Process.- 11. Limit Theorems for the Supercritical Case.- Complements and Problems IV.- V. Multi-Type Branching Processes.- 1. Introduction and Definitions.- 2. Moments and the Frobenius Theorem.- 3. Extinction Probability and Transience.- 4. Limit Theorems for the Subcritical Case.- 5. Limit Theorems for the Critical Case.- 6. The Supercritical Case and Geometric Growth.- 7. The Continuous Time, Multitype Markov Case.- 8. Linear Functionals of Supercritical Processes.- 9. Embedding of Urn Schemes into Continuous Time Markov Branching Processes.- 10. The Multitype Age-Dependent Process.- Complements and Problems V.- VI. Special Processes.- 1. A One Dimensional Branching Random Walk.- 2. Cascades; Distributions of Generations.- 3. Branching Diffusions.- 4. Martingale Methods.- 5. Branching Processes with Random Environments.- 6. Continuous State Branching Processes.- 7. Immigration.- 8. Instability.- Complements and Problems VI.- List of Symbols.- Author Index.