7 citations · 17 across the 7 of their papers we have counts for
8 papers
Martingale Methods for Maximal Large Deviations and Young Towers
José F. Alves, João S. Matias, Ian Melbourne
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we d…
Superdiffusive central limit theorems for geodesic flows on nonpositively curved surfaces
Yuri Lima, Carlos Matheus, Ian Melbourne
We prove a nonstandard central limit theorem and weak invariance principle, with superdiffusive normalisation , for geodesic flows on a class of nonpositively curv…
Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
Ian Melbourne, Zhe Wang
We obtain -Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows, where depends on the degree of nonuniformity. Utilizing a marting…
Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia
Yuri Lima, Carlos Matheus, Ian Melbourne
We consider a class of nonuniformly hyperbolic dynamical systems with a first return time satisfying a central limit theorem (CLT) with nonstandard normalisation .…
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems
Ilya Chevyrev, Alexey Korepanov, Ian Melbourne
We consider deterministic fast-slow dynamical systems of the form \[ x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} A(x_k^{(n)}) + n^{-1/α} B(x_k^{(n)}) v(y_k), \quad y_{k+1} = Ty_k, \] where…
Martingale-coboundary decomposition for families of dynamical systems
A. Korepanov, Z. Kosloff, I. Melbourne
We prove statistical limit laws for sequences of Birkhoff sums of the type where is a family of nonuniformly hyperbolic transformations. The…
On the detection of superdiffusive behaviour in time series
Georg A. Gottwald, Ian Melbourne
We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and determi…
Explicit coupling argument for nonuniformly hyperbolic transformations
A. Korepanov, Z. Kosloff, I. Melbourne
The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. Here it is verified that coupling yields explicit estimates that depend continuous…