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The maximum principle forms an important qualitative property of second order elliptic equations, therefore its discrete analogues, the so-called discrete maximum principles (DMPs) have drawn much attention. In this paper DMPs are…

Numerical Analysis · Mathematics 2018-07-05 János Karátson , Balázs Kovács , Sergey Korotov

We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…

Dynamical Systems · Mathematics 2010-01-11 Hongfei Cui

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…

Probability · Mathematics 2022-06-07 Peipei Gao , Yong Liu , Yue Sun , Zuohuan Zheng

We derive some large deviation bounds for events related to the "true self-repelling motion", a one-dimensional self-interacting process introduced by Toth and Werner, that has very different path properties than usual diffusion processes.…

Probability · Mathematics 2012-07-16 Laure Dumaz

We establish large deviation principles for the largest eigenvalue of large random matrices with variance profiles. For $N \in \mathbb N$, we consider random $N \times N$ symmetric matrices $H^N$ which are such that…

Probability · Mathematics 2024-03-25 Raphaël Ducatez , Alice Guionnet , Jonathan Husson

Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…

Dynamical Systems · Mathematics 2025-12-11 Sander C. Hille , Katarzyna Horbacz , Hanna Oppelmayer , Tomasz Szarek

In this paper, we first provide a criterion on uniform large deviation principles (ULDP) of stochastic differential equations under Lyapunov conditions on the coefficients, which can be applied to stochastic systems with coefficients of…

Probability · Mathematics 2024-02-27 Jifa Jiang , Jian Wang , Jianliang Zhai , Tusheng Zhang

Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…

Probability · Mathematics 2023-08-21 N. D. Vvedenskaya , A. V. Logachov , Y. M. Suhov , A. A. Yambartsev

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…

Probability · Mathematics 2021-06-24 Sarath Yasodharan , Rajesh Sundaresan

We obtain large deviations for a class of dependent random variables in the domain of attraction of an $\alpha$-stable law, $\alpha\in (0, 1)\cup (1, 2]$. This class includes ergodic sums of observables in the domain of attraction of an…

Probability · Mathematics 2024-06-18 Jonny Imbierski , Dalia Terhesiu

In this paper we study measurable dynamics for the widest reasonable class of smooth one dimensional maps. Three principle decompositions are described in this class : decomposition of the global measure-theoretical attractor into primitive…

Dynamical Systems · Mathematics 2016-09-06 Mikhail Lyubich

The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…

Probability · Mathematics 2007-05-23 Zongxia Liang

We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise.

Probability · Mathematics 2015-09-02 Zdzislaw Brzezniak , Sandra Cerrai

We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…

Statistics Theory · Mathematics 2015-03-13 Mengyu Xu , Danna Zhang , Wei Biao Wu

We develop a space-time large-deviation point of view on Gibbs-non-Gibbs transitions in spin systems subject to a stochastic spin-flip dynamics. Using the general theory for large deviations of functionals of Markov processes outlined in…

Probability · Mathematics 2015-03-17 Aernout van Enter , Roberto Fernández , Frank den Hollander , Frank Redig

We prove an large deviation principle for multivalued sdes

Probability · Mathematics 2011-04-28 Jiagang Ren , Siyan Xu , Xicheng Zhang

This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that…

Probability · Mathematics 2021-10-14 Jian Wang , Hao Yang , Jianliang Zhai , Tusheng Zhang

In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle…

Probability · Mathematics 2015-01-29 Kwabena Doku-Amponsah

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…

Statistical Mechanics · Physics 2015-05-13 Vladimir Y. Chernyak , Michael Chertkov , Sergey V. Malinin , Razvan Teodorescu

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…

Dynamical Systems · Mathematics 2024-05-28 Douglas Coates , Stefano Luzzatto , Muhammad Mubarak