The lifetime of a random set

We consider the lifetimes of systems that can be modeled as particles that move within a bounded region in ℝ n . Particles move within the set according to a random walk, and particles that leave the set are lost. We divide the set into equal cells and define the lifetime of the set as the time requ...

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Veröffentlicht in:	Journal of applied probability 2005-06, Vol.42 (2), p.566-580
Hauptverfasser:	Kiessler, Peter C., Nimitkiatklai, Kanoktip
Format:	Artikel
Sprache:	eng
Schlagworte:	60G70 90B25 Axiology Cubes Distribution theory Exact sciences and technology extreme value theory Integers interacting particle system Lifetime Limit theorems Markov processes Materials Mathematical lattices Mathematics Particle tracks Probability Probability and statistics Probability theory and stochastic processes Random variables Random walk Research Papers Sciences and techniques of general use Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications) Stochastic processes Studies Vertices Weibull distribution
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Beschreibung
Zusammenfassung:	We consider the lifetimes of systems that can be modeled as particles that move within a bounded region in ℝ n . Particles move within the set according to a random walk, and particles that leave the set are lost. We divide the set into equal cells and define the lifetime of the set as the time required for the number of particles in one of the cells to fall below a predetermined threshold. We show that the lifetime of the system, given a sufficiently large number of particles, is Weibull distributed.
ISSN:	0021-9002 1475-6072
DOI:	10.1239/jap/1118777188