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Interaction and Hierarchy in Measure-Valued Processes

In: Proceedings of the International Congress of Mathematicians

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  • Donald Dawson

    (Carleton University, Department of Mathematics and Statistics)

Abstract

Measure-valued Markov processes include both stochastic particle systems and an important class of stochastic partial differential equations. Examples of these arise in a variety of contexts such as mathematical genetics and reaction diffusion equations in random media. This paper will survey results on the long-time behavior of the class of critical measure-valued processes, that is, processes satisfying a mean conservation law. In the long-time limit processes of this type can develop an equilibrium structure or experience nonequilibrium cluster formation. The major objectives of this field are to give a precise description of these phenomena for special classes of critical systems and to develop an approach to classify such systems into broad “universality” classes that share the same large scale behaviors.

Suggested Citation

  • Donald Dawson, 1995. "Interaction and Hierarchy in Measure-Valued Processes," Springer Books, in: S. D. Chatterji (ed.), Proceedings of the International Congress of Mathematicians, pages 986-996, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9078-6_91
    DOI: 10.1007/978-3-0348-9078-6_91
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