9 citations · 29 across the 12 of their papers we have counts for
13 papers · 1 filter
Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability
Gerardo Barrera, Michael A. Högele
This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) Lévy…
Deviation frequencies of Brownian path property approximations
Michael A. Högele, Alexander Steinicke
This case study proposes a.s.~convergence quantifications of many classical sample path property approximations of Brownian motion in terms of the tradeoff between a.s.~rates and t…
Cutoff stability of multivariate geometric Brownian motion
G. Barrera, M. A. Högele, J. C. Pardo
This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation f…
Moment estimates in the first Borel-Cantelli Lemma with applications to mean deviation frequencies
Luisa F. Estrada, Michael A. Högele
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mea…
The cutoff phenomenon for the stochastic heat and the wave equation subject to small Lévy noise
G. Barrera, M. A. Högele, J. C. Pardo
This article generalizes the small noise cutoff phenomenon to the strong solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain sub…
The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise
G. Barrera, Michael A. Högele, J. C. Pardo
This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure…
Cutoff thermalization for Ornstein-Uhlenbeck systems with small Lévy noise in the Wasserstein distance
Gerardo Barrera, Michael A. Högele, Juan Carlos Pardo
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems wit…
How close are time series to power tail Lévy diffusions?
Jan Gairing, Michael A. Högele, Tania Kosenkova +1
This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driv…
Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications
Jan Gairing, Michael Högele, Tetiana Kosenkova
This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion…
Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves
Michael A. Högele, Paulo-Henrique da Costa
This article shows a strong averaging principle for diffusions driven by discontinuous heavy-tailed Lévy noise, which are invariant on the compact horizontal leaves of a foliated m…
A solution selection problem with small symmetric stable perturbations
Franco Flandoli, Michael Högele
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an -stable process. It is proved that…
Averaging along foliated Lévy diffusions
Michael Högele, Paulo R Ruffino
This article studies the dynamics of the strong solution of a SDE driven by a discontinuous Lévy process taking values in a smooth foliated manifold with compact leaves. It is assu…
Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise
Michael Högele, Ilya Pavlyukevich
We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability meas…