688 citations · 2.4k across the 52 of their papers we have counts for
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math.DS2020★ 1 cited
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
Alexey Korepanov, Zemer Kosloff, Ian Melbourne
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_…
math.DS2020★ 1 cited
Simulation of non-Lipschitz stochastic differential equations driven by -stable noise: a method based on deterministic homogenisation
Georg A. Gottwald, Ian Melbourne
We devise an explicit method to integrate -stable stochastic differential equations (SDEs) with non-Lipschitz coefficients. To mitigate against numerical instabilities caused by…
math.DS2020
Iterated invariance principle for slowly mixing dynamical systems
Matt Galton, Ian Melbourne
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsic…