Branching Stochastic Processes: Regulation, Regeneration, Estimation, Applications

2000 Mathematics Subject Classification: 60J80.This is a survey of the works of Bulgarian mathematicians in the area of Branching Stochastic Processes

Poisson Random Measures and Noncritical Multitype Markov Branching Processes

We investigate noncritical multi-type Markov branching processes with immigration generated by Poisson measures. Limiting distributions are obtained when the rates of the Poisson measures are asymptotically equivalent to exponential or regularly varying functions. In particular, results analogous to a strong LLN are presented, and limiting normal distributions are obtained when the rates increase. When the rates decrease, then conditional limiting distributions are established. A stationary limiting distribution is obtained when the mean Poisson measure grows linearly. The asymptotic behaviour of the first and second moments of the processes is also investigated.NFSR of the Ministry of Education and Science of Bulgaria, grant No. KP–06-H22/3

Critical Controlled Branching Processes And Their Relatives

This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Subcritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

[Mitov Kosto V.; Митов Косто В.]; [Yanev Nikolay M.; Janev N. M.; Janev Nikolaj; Янев Николай М.]The paper proposes an extension of Sevastyanov (1957) model based on a Markov branching process allowing an immigration component in the moments of a homogeneous Poisson process. Now Markov branching processes are also considered but assuming a time-nonhomogeneous Poisson immigration. These processes could be interpreted as models in cell proliferation kinetics with stem cell immigration. Limit theorems are proved in the subcritical case and new effects are obtained due to the non-homogeneity. 2000 Mathematics Subject Classification: 60J80