I. Melbourne

activity

20022023

most citedA New Test for Chaos

688 citations · 2.4k across the 52 of their papers we have counts for

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Showing math.PRShow all

3 papers · 1 filter

math.PR2020

Analytic proof of multivariate stable local large deviations and application to deterministic dynamical systems

Ian Melbourne, Dalia Terhesiu

We give a short analytic proof of local large deviations for i.i.d. random variables in the domain of a multivariate $α$ -stable law, $α \in (0, 1) \cup (1, 2]$ . Our method simultaneously…

math.PR2019★ 13 cited

Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2

Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2

We consider deterministic homogenization for discrete-time fast-slow systems of the form $X_{k + 1} = X_{k} + n^{- 1} a_{n} (X_{k}, Y_{k}) + n^{- 1/2} b_{n} (X_{k}, Y_{k}), Y_{k + 1} = T_{n} Y_{k}$ …

math.PR2014★ 7 cited

Deterministic homogenization for fast-slow systems with chaotic noise

David Kelly, Ian Melbourne

Consider a fast-slow system of ordinary differential equations of the form $x ˙ = a (x, y) + ε^{- 1} b (x, y)$ , $y ˙ = ε^{- 2} g (y)$ , where it is assumed that $b$ avera…