A Structured Markov Chain Approach to Branching Processes

作者：Hautphenne Sophie^*

来源：Stochastic Models, 2015, 31(3): 403-432.

DOI：10.1080/15326349.2015.1022264

• Branching process
• Quasi-birth-and-death process
• Random environment
• Markovian tree
• Matrix analytic methods

Algorithmic methods developed for structured Markov chains are extended to solve questions about a class of continuous-time branching processes called Markovian binary trees (MBTs). This approach allows us to compute the extinction probability of an MBT, the distribution of its maximal size given extinction, the expected time until extinction, and the mean time until the tree reaches a given size. The resulting algorithms are efficient in practice for processes of relatively small dimension. The numerical methods are illustrated on MBTs evolving in a Markovian random environment.

• 出版日期2015-7-3