688 citations · 2.4k across the 52 of their papers we have counts for
6 papers · 2 filters
A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion
Ian Melbourne, Paulo Varandas
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expand…
Mixing for invertible infinite measure systems
Ian Melbourne
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results…
Operator renewal theory for continuous time dynamical systems with finite and infinite measure
Ian Melbourne, Dalia Terhesiu
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of…
Central limit theorems and suppression of anomalous diffusion for systems with symmetry
Georg A. Gottwald, Ian Melbourne
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for obse…
Moment bounds and concentration inequalities for slowly mixing dynamical systems
Sébastien Gouëzel, Ian Melbourne
We obtain optimal moment bounds for Birkhoff sums, and optimal concentration inequalities, for a large class of slowly mixing dynamical systems, including those that admit anomalou…
Smooth approximation of stochastic differential equations
David Kelly, Ian Melbourne
Consider an Itô process satisfying the stochastic differential equation where are smooth and is a multidimensional Brownian motion. Suppose tha…