Killing and resurrection of Markov processes

Very simple renewal theory concepts are used to calculate transition probabilities, and their limits, for a Markov process subjected to an independent Poisson process of killing events which reset the process to the zero state. A particular case, treated heretofore by more restrictive methods, is where the basic process has an absorbing zero state from which it can be resurrected. Simple examples illustrate the scope of the basic formulation

[1]  Eric Renshaw,et al.  Birth-death processes with mass annihilation and state-dependent immigration , 1997 .

[2]  A. Pakes,et al.  Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state , 1995, Advances in Applied Probability.

[3]  E. G. Kyriakidis.  Stationary probabilities for a simple immigration-birth-death process under the influence of total catastrophes , 1994 .

[4]  Anthony G. Pakes.  EXPLOSIVE MARKOV BRANCHING PROCESSES: ENTRANCE LAWS AND LIMITING BEHAVIOUR , 1993 .

[5]  Eric Renshaw,et al.  Existence and uniqueness criteria for conservative uni-instantaneous denumerable Markov processes , 1993 .

[6]  Absorbing Markov and branching processes with instantaneous resurrection , 1993 .

[7]  E. G. Kyriakidis.  A Markov decision algorithm for optimal pest control through uniform catastrophes , 1993 .

[8]  W. J. Anderson.  Continuous-Time Markov Chains , 1991 .

[9]  P. Pollett.  A note on the classification of Q-processes when Q is not regular , 1990, Journal of Applied Probability.

[10]  A. Pakes.  The Markov branching process with density-independent catastrophes. III. The supercritical case , 1990, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  W. Ewens.  Mathematical Population Genetics , 1980 .

[12]  A. Pakes.  On the age distribution of a Markov chain , 1978, Journal of Applied Probability.

[13]  M. Yamazato.  Some results on continuous time branching processes with state-dependent immigration , 1975 .

[14]  Norman T. J. Bailey,et al.  The Elements of Stochastic Processes with Applications to the Natural Sciences , 1964 .