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A limit theorem for certain disordered random systems

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Xinhong Ding
Xinhong Ding*
Affiliation:
Carleton University
*
* Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada.
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Abstract

Many disordered random systems in applications can be described by N randomly coupled Ito stochastic differential equations in :

where is a sequence of independent copies of the one-dimensional Brownian motion W and ( is a sequence of independent copies of the ℝp-valued random vector ξ. We show that under suitable conditions on the functions b, σ, K and Φ the dynamical behaviour of this system in the N → (limit can be described by the non-linear stochastic differential equation

where P(t, dx dy) is the joint probability law of ξ and X(t).

Keywords

INTERACTING DIFFUSIONSMCKEAN-VLASOV LIMITNEURAL NETWORKS: SPIN GLASSES

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 1022 - 1043
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by Professor Donald A. Dawson's research grant.

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