scholarly journals Birkhoff’s individual ergodic theorem and maximal ergodic theorem for fuzzy dynamical systems

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Dagmar Markechová ◽  
Anna Tirpáková
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Individual Ergodic Theorem ◽  
Fuzzy Dynamical Systems

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

2017 ◽  
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Ergodic Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematics Students ◽  
Intuitionistic Fuzzy ◽  
Individual Ergodic Theorem ◽  
Recurrence Theorem ◽  
The Individual ◽  
Atanassov Intuitionistic Fuzzy Sets

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

Induced transformations of recurrent a.m.s. dynamical systems

2015 ◽  
Vol 15 (02) ◽  
pp. 1550010
Author(s):  
Sheng Huang ◽  
Mikael Skoglund
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Random Process ◽  
Ergodic Theorem ◽  
Finite Measure ◽  
Stationary Random Process ◽  
Finite State ◽  
Ratio Ergodic Theorem

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process. As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

ON THE ABSOLUTE REGULARITY OF LINEAR RANDOM DYNAMICAL SYSTEMS

2003 ◽  
Vol 03 (04) ◽  
pp. 453-461 ◽  
Author(s):  
LUU HOANG DUC
Keyword(s):  
Dynamical Systems ◽  
Ergodic Theorem ◽  
Random Dynamical Systems ◽  
Absolute Regularity ◽  
Integrability Conditions ◽  
Multiplicative Ergodic Theorem ◽  
Lyapunov Regularity ◽  
The Absolute

We introduce a concept of absolute regularity of linear random dynamical systems (RDS) that is stronger than Lyapunov regularity. We prove that a linear RDS that satisfies the integrability conditions of the multiplicative ergodic theorem of Oseledets is not merely Lyapunov regular but absolutely regular.

Stability of fuzzy dynamical systems based on quasi-level-wise system

2017 ◽  
Vol 33 (6) ◽  
pp. 3515-3528 ◽  
Author(s):  
Debnarayan Khatua ◽  
Kalipada Maity
Keyword(s):  
Dynamical Systems ◽  
Fuzzy Dynamical Systems
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