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Construction Of Markovian Coalescents (1997)
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| Venue: | Ann. Inst. Henri Poincar'e |
| Citations: | 48 - 16 self |
BibTeX
@ARTICLE{Evans97constructionof,
author = {Steve N. Evans and Jim Pitman},
title = {Construction Of Markovian Coalescents},
journal = {Ann. Inst. Henri Poincar'e},
year = {1997},
volume = {34},
pages = {339--383}
}
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Abstract
Partition-valued and measure-valued coalescent Markov processes are constructed whose state describes the decomposition of a finite total mass m into a finite or countably infinite number of masses with sum m, and whose evolution is determined by the following intuitive prescription: each pair of masses of magnitudes x and y runs the risk of a binary collision to form a single mass of magnitude x+y at rate (x; y), for some non-negative, symmetric collision rate kernel (x; y). Such processes with finitely many masses have been used to model polymerization, coagulation, condensation, and the evolution of galactic clusters by gravitational attraction. With a suitable choice of state space, and under appropriate restrictions on and the initial distribution of mass, it is shown that such processes can be constructed as Feller or Feller-like processes. A number of further results are obtained for the additive coalescent with collision kernel (x; y) = x + y. This process, which arises fro...
Keyphrases
markovian coalescents state space symmetric collision rate kernel appropriate restriction finite total mass feller-like process binary collision additive coalescent many mass gravitational attraction collision kernel suitable choice galactic cluster infinite number initial distribution following intuitive prescription measure-valued coalescent markov process single mass
