scholarly journals Invariance Principle on the Slice

2018 ◽  
Vol 10 (3) ◽  
pp. 1-37
Author(s):  
Yuval Filmus ◽  
Guy Kindler ◽  
Elchanan Mossel ◽  
Karl Wimmer
Keyword(s):  
Invariance Principle

scholarly journals Mixing rates for potentials of non-summable variations

2021 ◽  
pp. 1-18
Author(s):  
CHRISTOPHE GALLESCO ◽  
DANIEL Y. TAKAHASHI
Keyword(s):  
Invariance Principle ◽  
Type Inequality ◽  
Upper Bounds ◽  
Decay Of Correlations ◽  
Relaxation Rates ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
Coupling Inequality ◽  
Mixing Rates

Abstract Mixing rates, relaxation rates, and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. This paper exhibits upper bounds for these quantities for dynamics defined by potentials with square-summable variations. We obtain these bounds as corollaries of a new block coupling inequality between pairs of dynamics starting with different histories. As applications of our results, we prove a new weak invariance principle and a Hoeffding-type inequality.

Markovian random iterations of homeomorphisms of the circle

2021 ◽  
pp. 1-22
Author(s):  
EDGAR MATIAS
Keyword(s):  
Markov Chains ◽  
Invariance Principle ◽  
Exponential Synchronization ◽  
Type Result

Abstract In this paper we prove a local exponential synchronization for Markovian random iterations of homeomorphisms of the circle $S^{1}$ , providing a new result on stochastic circle dynamics even for $C^1$ -diffeomorphisms. This result is obtained by combining an invariance principle for stationary random iterations of homeomorphisms of the circle with a Krylov–Bogolyubov-type result for homogeneous Markov chains.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

Invariance principle for certain classes of random fields

1980 ◽  
Vol 31 (5) ◽  
pp. 443-448
Author(s):  
N. N. Leonenko ◽  
M. I. Yadrenko
Keyword(s):  
Invariance Principle ◽  
Random Fields

scholarly journals Adaptive Feedback Control for Synchronization of Chaotic Neural Systems with Parameter Mismatches

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Qian Ye ◽  
Zhengxian Jiang ◽  
Tiane Chen
Keyword(s):  
Feedback Control ◽  
Invariance Principle ◽  
Neural Systems ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Synchronization Problem ◽  
Feedback Method

This work pertains to the study of the synchronization problem of a class of coupled chaotic neural systems with parameter mismatches. By means of an invariance principle, a rigorous adaptive feedback method is explored for synchronization of a class of coupled chaotic delayed neural systems in the presence of parameter mismatches. Finally, the performance is illustrated with simulations in a two-order neural systems.

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