Limit Laws For Critical Decomposable Branching Processes

Branching processes are widely used and are important branches of stochastic processes.In this paper,we introduce the theory of decomposable branching pro-cess,including classical Galton-Watson branching process,definition of decomposable branching process,generating function,extinction probability and so on.The extinc-tion velocity of particles and the limit law for generating function are studied.As we all know,the extinction probability of critical branching process is 1.we assume that process is extinct at time n and study the probability of extinct time.we also study the conditional expectation of particle number.