Almost sure invariance principle for random dynamical systems via Gouëzel's approach

Dragičević, Davor; Hafouta, Yeor

doi:10.1088/1361-6544/ac14a1

Cited by 19 publications

(8 citation statements)

References 59 publications

(155 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, their results rely on a moderate deviation result for stationary Markov chains by Wu and Zhao in [36], which seems not to be available for inhomogeneous Markov chains. Moreover, Dragičević and Hafouta [14] and Hafouta [16] obtained a vector valued almost sure invariance principle for the sequential iteration of non-uniformly expanding maps. There, the authors obtain a better rate of approximation by assuming an abstract condition on the characteristic functions of the associated process.…”

Section: Dρ(ω)mentioning

confidence: 99%

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

Stadlbauer

Varandas

Zhang³

2022

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

We find generalized conformal measures and equilibrium states for random dynamics generated by Ruelle expanding maps, under which the dynamics exhibits exponential decay of correlations. This extends results by Baladi [Correlation spectrum of quenched and annealed equilibrium states for random expanding maps. Comm. Math. Phys.186 (1997), 671–700] and Carvalho et al [Semigroup actions of expanding maps. J. Stat. Phys.116(1) (2017), 114–136], where the randomness is driven by an independent and identically distributed process and the phase space is assumed to be compact. We give applications in the context of weighted non-autonomous iterated function systems, free semigroup actions and introduce a boundary of equilibria for not necessarily free semigroup actions.

show abstract

Section: Dρ(ω)mentioning

confidence: 99%

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

Stadlbauer

Varandas

Zhang³

2022

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

show abstract

“…Until now, constrained control algorithms have been investigated by some researchers. The existing constraint control methods mainly include: set invariance principle, 13,14 command governor, 15,16 reference governor, 17,18 extremum seeking control, 19 model predictive control, 20–23 etc. However, there are some limitations in these algorithms.…”

Section: Introductionmentioning

confidence: 99%

A wheel slip ratio constraint control for ABS based on Tangent Type Barrier Lyapunov Function

Wang

Liu

Wei

et al. 2022

Measurement and Control

View full text Add to dashboard Cite

This paper is concerned with the problem of a wheel slip ratio constraint control for the Antilock Braking System (ABS) with external interferences and state constraints. A quarter vehicle braking model with uncertainties is considered, and a constraint control method based on Tangent Type Barrier Lyapunov Function (Tan-BLF) is designed. In addition, due to the selection of the appropriate adaptive control rate, the designed control method can quickly track the ideal slip ratio and ensure that the slip ratio for ABS is always constrained in the stable region even if there are uncertainties in the control system and unknown external disturbances. The simulation results show that the control scheme proposed in this paper, compared with the traditional QLF controller scheme, can make the vehicle wheel slip rate stable at the optimal value early and keep it in the optimal range from the beginning of the simulation, thus reducing the braking distance and braking time of the vehicle, which means that the vehicle can avoid wheel locking. And the adaptive rate is always bounded.

show abstract

“…Since then quenched limit theorems for random dynamical systems have been extensively studied. For instance, in [16,[20][21][22] almost sure invariance principle (ASIP, an almost sure approximation by a sum of independent Gaussians) was established for random expanding or hyperbolic maps T ω , in [19,31] Berry-Esseen theorems (optimal rates in the CLT) were obtained for similar classes of maps and in [17,18,23,31] local CLTs were achieved. In addition, in [27] several limit theorems were extended to random non-uniformly hyperbolic or expanding maps.…”

mentioning

confidence: 99%

Large deviations, moment estimates and almost sure invariance principles for skew products with mixing base maps and expanding-on-average fibers

Hafouta

2023

Ergod. Th. Dynam. Sys.

View full text Add to dashboard Cite

In this paper we show how to apply classical probabilistic tools for partial sums $\sum _{j=0}^{n-1}\varphi \circ \tau ^j$ generated by a skew product $\tau $ , built over a sufficiently well-mixing base map and a random expanding dynamical system. Under certain regularity assumptions on the observable $\varphi $ , we obtain a central limit theorem (CLT) with rates, a functional CLT, an almost sure invariance principle (ASIP), a moderate-deviations principle, several exponential concentration inequalities and Rosenthal-type moment estimates for skew products with $\alpha $ -, $\phi $ - or $\psi $ -mixing base maps and expanding-on-average random fiber maps. All of the results are new even in the uniformly expanding case. The main novelty here (in contrast to [2]) is that the random maps are not independent, they do not preserve the same measure and the observable $\varphi $ depends also on the base space. For stretched exponentially ${\alpha }$ -mixing base maps our proofs are based on multiple correlation estimates, which make the classical method of cumulants applicable. For $\phi $ - or $\psi $ -mixing base maps, we obtain an ASIP and maximal and concentration inequalities by establishing an $L^\infty $ convergence of the iterates ${\mathcal K}^{\,n}$ of a certain transfer operator ${\mathcal K}$ with respect to a certain sub- ${\sigma }$ -algebra, which yields an appropriate (reverse) martingale-coboundary decomposition.

show abstract

Almost sure invariance principle for random dynamical systems via Gouëzel's approach

Cited by 19 publications

References 59 publications

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

Quenched and annealed equilibrium states for random Ruelle expanding maps and applications

A wheel slip ratio constraint control for ABS based on Tangent Type Barrier Lyapunov Function

Large deviations, moment estimates and almost sure invariance principles for skew products with mixing base maps and expanding-on-average fibers

Contact Info

Product

Resources

About