688 citations · 2.4k across the 52 of their papers we have counts for
5 papers · 1 filter
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 -stable law, . Our method simultaneously…
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_…
St. Petersburg paradox for quasiperiodically hypermeandering spiral waves
Vadim N. Biktashev, Ian Melbourne
It is known that quasiperiodic hypermeander of spiral waves almost certainly produces a bounded trajectory for the spiral tip. We analyse the size of this trajectory. We show that…
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…
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…