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2 results

On the entropy for semi-Markov processes
Part of
Valerie Girardin, Nikolaos Limnios
Journal:

Journal of Applied Probability / Volume 40 / Issue 4 / September 2003

Published online by Cambridge University Press:

14 July 2016, pp. 1060-1068

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September 2003
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The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

The propagation of chaos of multitype mean field interacting particle systems
Part of
Shui Feng
Journal:

Journal of Applied Probability / Volume 34 / Issue 2 / June 1997

Published online by Cambridge University Press:

14 July 2016, pp. 346-362

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June 1997
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A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.

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2 results

On the entropy for semi-Markov processes

The propagation of chaos of multitype mean field interacting particle systems