## Construction Of Markovian Coalescents (1997)

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Venue: | Ann. Inst. Henri Poincar'e |

Citations: | 44 - 20 self |

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@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...