Markov branching processes with disasters: extinction, survival and duality to pjump processes
Abstract
A $p$jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of timehomogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for timeinhomogeneous birthdeath processes underlying timedependent binomial disasters and continuous state branching processes with $p$jumps.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 arXiv:
 arXiv:1808.00073
 Bibcode:
 2018arXiv180800073H
 Keywords:

 Mathematics  Probability;
 60J80 (Primary) 60J75;
 60F10 (Secondary)
 EPrint:
 27 pages