5 papers
Big jump principle for heavy-tailed random walks with correlated increments
Marc Höll, Eli Barkai
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heav…
Large deviations of the ballistic Lévy walk model
Wanli Wang, Marc Höll, Eli Barkai
We study the ballistic Lévy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a…
Extreme value theory for constrained physical systems
Marc Höll, Wanli Wang, Eli Barkai
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin mode…
Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average
Marc Höll, Ken Kiyono, Holger Kantz
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduce…
Probabilistic properties of detrended fluctuation analysis for Gaussian processes
G. Sikora, M. Hoell, A. Wylomanska +3
The detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range correlations in time series. Although DFA has found many interesting a…