Comparison of interacting diffusions and an application to their ergodic theory

J. Theodore Cox; Klaus Fleischmanm; Andreas Greven

doi:10.1007/BF01191911

Comparison of interacting diffusions and an application to their ergodic theory

J. Theodore Cox, Klaus Fleischmanm, Andreas Greven

Department of Mathematics

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41 Scopus citations

Abstract

A general comparison argument for expectations of certain multitime functionals of infinite systems of linearly interacting diffusions differing in the diffusion coefficient is derived. As an application we prove clustering occurs in the case when the symmetrized interaction kernel is recurrent, and the components take values in an interval bounded on one side. The technique also gives an alternative proof of clustering in the case of compact intervals.

Original language	English (US)
Pages (from-to)	513-528
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	105
Issue number	4
DOIs	https://doi.org/10.1007/BF01191911
State	Published - Aug 1996

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF01191911

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abstract = "A general comparison argument for expectations of certain multitime functionals of infinite systems of linearly interacting diffusions differing in the diffusion coefficient is derived. As an application we prove clustering occurs in the case when the symmetrized interaction kernel is recurrent, and the components take values in an interval bounded on one side. The technique also gives an alternative proof of clustering in the case of compact intervals.",

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AB - A general comparison argument for expectations of certain multitime functionals of infinite systems of linearly interacting diffusions differing in the diffusion coefficient is derived. As an application we prove clustering occurs in the case when the symmetrized interaction kernel is recurrent, and the components take values in an interval bounded on one side. The technique also gives an alternative proof of clustering in the case of compact intervals.

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Comparison of interacting diffusions and an application to their ergodic theory

Abstract

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