Branching processes and its estimation theory
Delivers a systematic account of the branching process, with special emphasis on developments that have taken place since 1972. Unifies the several methods given in different research papers and journals. The book is divided into two parts. Part I comprises five chapters dealing with the various types of ordinary branching process, such as Galton-Watson branching process, Markov branching process, Bellman-Harris branching process, and branching process with random environments. Part II offers a more detailed look at specific questions associated with branching processes and discusses subjects currently under investigation. Topics covered include branching processes with immigration, branching process with disasters, estimation theory in branching processes, and branching processes and renewal theory. Contains many examples, exercises and summaries.
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MARKOV BRANCHING PROCESS
BELLMANHARRIS BRANCHING PROCESS
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age-dependent branching process Assume asymptotic behaviour Athreya and Kaplan Athreya and Ney Bellman-Harris process bounded completes the proof consider continuous converges almost surely converges in distribution critical defined dependent branching process distribution function ergodic estimators extinction Feller following result following theorem functional equation Galton-Watson process given Hence Heyde identically distributed random implies independent and identically integral equation Jagers Keiding Krishnamoorthy Laplace transform law of large lim sup limit theorem limiting distribution Malthusian parameter Markov branching process Markov chain Markov process martingale Math matrix non-decreasing non-degenerate non-lattice non-negative number of individuals number of particles obtain offspring distribution Pakes population Prob probability generating function process with immigration process with random proof of theorem proved the following random environments random variables renewal equation Riemann integrable Sankaranarayanan Seneta shown slowly varying stochastic subcritical supercritical Suppose uniformly vector zero