Statistical properties of a skew product with a curve of neutral points

By S. Gouëzel. Ergodic Theory and Dynamical Systems, 2003

50 citations recorded by the source corpus.

We study a skew product with a curve of neutral points. We show that there exists a unique absolutely continuous invariant probability measure, and that the Birkhoff averages of a sufficiently smooth observable converge to a normal law or a stable law, depending on the average of the observable along the neutral curve.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/17a40a18ae05c4c2b138fb110f34ed0a3a1d29ea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Ian Melbourne
2. David Kelly
3. Mark Holland

In Statistics and Probability

1. David Kelly
2. Mark Holland
3. Ian Melbourne

Citations in the corpus

• Central limit theorems and invariance principles for Lorenz attractors (2007, methodology): “The approach in [12] was used by Gouëzel [6] and by Melbourne and Nicol [11] to prove, respectively, the CLT and stable laws, and the ASIP, for classes of nonuniformly hyperbolic flows.”
• Smooth approximation of stochastic differential equations (2014, background): “1 below is formulated in a purely probabilistic setting, extending the approach in [19, 37, 40].”