Statistics Seminars: Uniqueness and extinction properties of weighted collision branching processes
27 May 2005 00:00 in CM107
"Different from the Markov branching process, the weighted collision branching process is an interacting branching system. The basic properties regarding uniqueness, extinction and explosion behaviour of such system are addressed in this talk. It is proved that the super-explosive weighted collision branching process is honest if and only if the mean death rate is greater than or equal to the mean birth rate while the sub-explosive one is almost honest. Explicit expressions for the extinction probability, the mean and the conditional mean extinction times are presented. The explosion behaviour of such interacting branching models is investigated and an explicit expression for mean explosive time is established. It is revealed that these basic properties are substantially different between the super-explosive and sub-explosive weighted collision branching processes.
"CM221, 2.15 - 3.00 pm"
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