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A limit theorem for certain disordered random systems
- Part of
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- Journal:
- Advances in Applied Probability / Volume 26 / Issue 4 / December 1994
- Published online by Cambridge University Press:
- 01 July 2016, pp. 1022-1043
- Print publication:
- December 1994
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- Article
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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).
:
is a sequence of independent copies of the one-dimensional Brownian motion 
