Zobrazeno 1 - 10
of 110
pro vyhledávání: '"Högele, Michael"'
This article shows a stochastic version of the Schauder-Tychonoff fixed-point theoren and yields a stochastically weak solution to a large class of systems of nonlinear reaction-diffusion type equations driven by a cylindrical Wiener process and a Po
Externí odkaz:
http://arxiv.org/abs/2312.00927
In this article we quantify almost sure martingale convergence theorems in terms of the tradeoff between asymptotic almost sure rates of convergence (error tolerance) and the respective modulus of convergence. For this purpose we generalize {an} elem
Externí odkaz:
http://arxiv.org/abs/2310.09055
Autor:
Barrera, Gerardo, Högele, Michael A.
Publikováno v:
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2023, Volume 33, Number 11, 113124
This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) L\'evy noise at fixed noise intensity. The results are based on several er
Externí odkaz:
http://arxiv.org/abs/2306.11616
Publikováno v:
Journal of Statistical Physics 2024
This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein-Kantorovich-Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration
Externí odkaz:
http://arxiv.org/abs/2302.13968
This case study proposes robustness quantifications of many classical sample path properties of Brownian motion in terms of the (mean) deviation frequencies along typical a.s.~approximations. This includes L\'evy's construction of Brownian motion, th
Externí odkaz:
http://arxiv.org/abs/2302.04115
Autor:
Estrada, Luisa F., Högele, Michael A.
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 mean deviation frequencies in the Strong Law and the Law of the Iterated
Externí odkaz:
http://arxiv.org/abs/2204.04369
Publikováno v:
Journal of Dynamics and Differential Equations 2022, 1-28
This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a unique coercive stable fixed point subject to general additive Markovian noise in the limit of small noise inte
Externí odkaz:
http://arxiv.org/abs/2108.08351
Publikováno v:
Electronic Journal of Probability 2021, Volume 26, Number 119, 2021, 1-76
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 jump L\'evy noise of small amplitude $\varepsilon>0$, where the drivin
Externí odkaz:
http://arxiv.org/abs/2011.10806
Publikováno v:
Journal of Statistical Physics 2021, Volume 184, Number 27, 1-54
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems $(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy noise and initial value $x$. The
Externí odkaz:
http://arxiv.org/abs/2009.10590
We establish Freidlin-Wentzell results for a nonlinear ordinary differential equation starting close to the stable state $0$, say, subject to a perturbation by a stochastic integral which is driven by an $\varepsilon$-small and $(1/\varepsilon)$-acce
Externí odkaz:
http://arxiv.org/abs/1904.02125