Abstract:

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the
concepts of the multitype canonical Markov branching chain in random
environment (CMBCRE) and multitype Markov branching chain in random
environment (MBCRE) and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

Key words: Random Markov matrix, Markov chain in random environment, Markov branching chain in random environment, canonical Markov branchingchain in random environment, generator random variables