Linear birth and death processes under the influence of disasters with time-dependent killing probabilities

Nan Fu Peng, Dennis Keith Pearl, Wenyaw Chan, Robert Bartoszyński

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Supercritical linear birth-and-death processes are considered under the influence of disasters that arrive as a renewal process independently of the population size. The novelty of this paper lies in assuming that the killing probability in a disaster is a function of the time that has elapsed since the last disaster. A necessary and sufficient condition for a.s. extinction is found. When catastrophes form a Poisson process, formulas for the Laplace transforms of the expectation and variance of the population size as a function of time as well as moments of the odds of extinction are derived (these odds are random since they depend on the intercatastrophe times). Finally, we study numerical techniques leading to plots of the density of the probability of extinction.

Original languageEnglish (US)
Pages (from-to)243-258
Number of pages16
JournalStochastic Processes and their Applications
Volume45
Issue number2
DOIs
StatePublished - Jan 1 1993

Fingerprint

Birth and Death Process
Linear Process
Disaster
Extinction
Disasters
Odds
Population Size
Catastrophe
Renewal Process
Laplace transforms
Numerical Techniques
Poisson process
Laplace transform
Moment
Necessary Conditions
Sufficient Conditions
Influence

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

Cite this

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abstract = "Supercritical linear birth-and-death processes are considered under the influence of disasters that arrive as a renewal process independently of the population size. The novelty of this paper lies in assuming that the killing probability in a disaster is a function of the time that has elapsed since the last disaster. A necessary and sufficient condition for a.s. extinction is found. When catastrophes form a Poisson process, formulas for the Laplace transforms of the expectation and variance of the population size as a function of time as well as moments of the odds of extinction are derived (these odds are random since they depend on the intercatastrophe times). Finally, we study numerical techniques leading to plots of the density of the probability of extinction.",
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Linear birth and death processes under the influence of disasters with time-dependent killing probabilities. / Peng, Nan Fu; Pearl, Dennis Keith; Chan, Wenyaw; Bartoszyński, Robert.

In: Stochastic Processes and their Applications, Vol. 45, No. 2, 01.01.1993, p. 243-258.

Research output: Contribution to journalArticle

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