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MS Mon. Series
Limit Theorems and Transient Phenomena in the Theory of Branching Processes
Soltan Aliev, Yaroslav I. Yeleyko, Iryna B. Bazylevych
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[ Contents ]
In this monograph, there are presented two directions of the theory of branching processes, namely, the processes with arbitrary numbers types of particles and processes with continuous state space.
The monograph consists of eight chapters. The first one contains a short historical information about branching processes and concise review of literature. The second one is devoted to the basic definition and statements of theorems. The third chapter contains the results of an article by M. Jirina ôGeneral branching process with continuous time parameter''.
Further, there are presented the results of Ya. Yeleyko, the limit theorems for processes with arbitrary numbers of particles. The fifth chapter follows the fundamental article of M. Jirina ôStochastic branching processes with continuous state spaceö as well as Yu. Ryshov and A. Skorohod ôHomogeneous branching processes with finite number types of particles and continuously changing massö'. The final chapters include theorems on convergence of sequences of Galton-Watson processes to a process with continuous state space.
Mathematical Studies: Monograph Series. Volume 14
Brief review of literature
Theoretical information (Processes with one type of particles. Multitype branching processes. The processes with immigration. Renewal equation.)
General branching process ( Introduction. Processes with continuous time. The homogeneous case.)
Arbitrary number of types (Equations of renewal. Limiting theorems. Transitional phenomena. Processes with immigration. Asymptotic of mathematical expectation. Asymptotic of maximum proper value.)
Continuous state space ( Introduction. B-process with discrete time. BP with continuous state space. Cumulant of processes.)
Equitype processes (Galton-Watson processes. Near-critical Galton-Watson process. Processes with immigration. Bellman-Harris critical processes. Convergence of Bellman-Harris processes.)
Multitype processes (Convergence to multitype process. Convergence to one-dimensional process. Processes which depend on age. Multivariate processes. Processes with continuous time.)
Countable number of types.
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