Ergodic properties of max-infinitely divisible processes

By Zakhar Kabluchko, Martin Schlather. 2009

55 citations recorded by the source corpus.

We prove that a stationary max-infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max-infinitely divisible processes.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66be45de0c7f4a72e06466389e2d0c12519cda84

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In Finance

In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Mixing properties of max-stable processes are characterized by the value of the extremal coefficient θ(s1, s2) as the lag distance ‖h‖ = ‖s2 − s1‖ tends to infinity (Kabluchko and Schlather, 2010).”
Conditional simulation of max-stable processes (2012, background): “Since the considereBrown–Resnick processes are ergodic (Kabluchko and Schlather, 2010), for regions far away from any conditioning location the sample quantiles converges to that of a standard Gumbel distribution indicating that the conditional event has no influence.”
On the structure and representations of max-stable processes (2009, background): “See also the recent work of Kabluchko and Schlather [15].”
Simulation of Brown–Resnick processes (2012, background): “Ergodic properties of the processes are studied by Kabluchko (2009b) and Wang and Stoev (2009) who discuss the decomposition into conservative and dissipative components; ergodicity and mixing properties are investigated by Kabluchko and Schlather (2009).”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, background): “However, the Schlather model is not ergodic in the sense that it cannot attain independence of Z(x1) and Z(x2) unless corr{ε(x1), ε(x2)} = −1; equivalently its extremal coefficient θ(h) is bounded below 2 for any h (Kabluchko and Schlather 2010; Davison and Gholamrezaee 2012).”