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Some condensation processes of McKean type

Published online by Cambridge University Press:  14 July 2016

Frank B. Knight
Frank B. Knight*
Affiliation:
University of Illinois at Urbana-Champaign
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Extract

In a short article McKean [2] inaugurated the study of a class of time-inhomogeneous Markov processes which arise from the reaction of a single particle (the “tagged” particle) with an evolving environment of other particles. Other more recent references on these processes are [1], [4] and [5], in which some existence and uniqueness theorems for the solution of the resulting non-linear equation are obtained. We confine attention here to a very particular type of these processes which arises when two interacting particles simply coalesce, and the mass is taken as the process variable.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 399 - 406
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Johnson, D. P. (1968) On a class of stochastic processes and its relationship in infinite particle gasses. Trans. Amer. Math. Soc. 132, 275–295.Google Scholar
[2] Mckean, H. P. Jr. (1966) A class of Markov processes associated with nonlinear parabolic equations. Proc. Nat. Acad. Sci. 56, 1907–1911.Google Scholar
[3] Melzak, Z. A. (1953) The effect of coalescence in certain collision processes. Quart. J. Appl. Math. 11, 231–234.Google Scholar
[4] Ueno, T. (1969) A class of Markov processes with non-linear, bounded generators. Japan. J. Math. 38, 19–38.CrossRefGoogle Scholar
[5] Ueno, T. (1969) A class of purely discontinuous Markov processes with interactions, I. Proc. Japan Acad. 45, 348–353.Google Scholar