English
Related papers

Related papers: Almost sure invariance principle for dynamical sys…

200 papers

Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…

Probability · Mathematics 2014-07-15 Vladimir Belitsky , Mikhail Menshikov , Dimitri Petritis , Marina Vachkovskaia

We show an invariance principle for rescaled clocks of positive semi-stable Markov processes, proving a conjecture presented in Remark 4 in Demni, Rouault, Zani [11], 2015.

Probability · Mathematics 2020-11-23 Maria-Emilia Caballero , Alain Rouault

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…

Systems and Control · Electrical Eng. & Systems 2023-06-27 Adnane Saoud , Murat Arcak

We devise an abstract, modular scheme to prove continuity of the Lyapunov exponents for a general class of linear cocycles. The main assumption is the availability of appropriate large deviation type (LDT) estimates which are uniform in the…

Dynamical Systems · Mathematics 2015-07-13 Pedro Duarte , Silvius Klein

We prove an almost sure invariance principle for the capacity and the cardinality of the range of a class of $\alpha$-stable random walks on the integer lattice $\mathbb{Z}^d$ with $d/\alpha > 5/2$, and $d/\alpha >3/2$, respectively. As a…

Probability · Mathematics 2023-06-01 Wojciech Cygan , Nikola Sandrić , Stjepan Šebek

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

Optimization and Control · Mathematics 2022-06-13 Yonathan Efroni , Sham Kakade , Akshay Krishnamurthy , Cyril Zhang

In many interacting particle systems, tagged particles move diffusively upon subtracting a drift. General techniques to prove such `invariance principles' are available for reversible processes (Kipnis-Varadhan) and for non-reversible…

Probability · Mathematics 2016-10-26 Nick Crawford , Wojciech De Roeck

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…

Probability · Mathematics 2026-02-03 Simona Diaconu

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors…

Quantum Physics · Physics 2024-02-13 Tibor Rakovszky , Sarang Gopalakrishnan , Curt von Keyserlingk

This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…

Machine Learning · Computer Science 2024-03-04 Igor Pontes Duff , Pawan Goyal , Peter Benner

Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing various regularity properties such as metric regularity, i.e., the openness with a linear rate around the reference point, of…

Functional Analysis · Mathematics 2023-09-07 Radek Cibulka

In the recent article D\"oring et al. [4] the authors conditioned a stable process with two-sided jumps to avoid an interval. As usual the strategy was to find an invariant function for the process killed on entering the interval and to…

Probability · Mathematics 2020-02-19 Pierre Lenthe , Philip Weissmann

In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…

Dynamical Systems · Mathematics 2025-09-22 Bryn Davies , Angelica Yu Xiao

We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…

Dynamical Systems · Mathematics 2007-05-23 Ivan Tyukin , Danil Prokhorov , Cees van Leeuwen

Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…

Optimization and Control · Mathematics 2009-07-24 Iasson Karafyllis

We prove a weak iterated invariance principle for a large class of non-uniformly expanding random dynamical systems. In addition, we give a quenched homogenization result for fast-slow systems in the case when the fast component corresponds…

Dynamical Systems · Mathematics 2025-02-11 Davor Dragicevic , Yeor Hafouta

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

Machine Learning · Computer Science 2017-08-11 Daniil Ryabko

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

Probability · Mathematics 2024-11-21 Paweł J. Szabłowski

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter…

Statistics Theory · Mathematics 2014-12-01 Kevin McGoff , Sayan Mukherjee , Andrew Nobel , Natesh Pillai

Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…

Statistics Theory · Mathematics 2008-06-30 Keh-Shin Lii , Murray Rosenblatt