Functional correlation bounds and deterministic homogenisation of fast-slow systems
Abstract
We give elementary and explicit sufficient conditions (in particular, a functional correlation bound) for deterministic homogenisation (convergence to a stochastic differential equation) for discrete-time fast-slow systems of the form \[ xk+1 = xk + n-1an(xk,yk) + n-1/2bn(xk,yk), yk+1=Tn yk. \] We then prove that these sufficient conditions are satisfied by various examples of nonuniformly hyperbolic dynamical systems Tn .
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