NDLI: Dynamical Entropy for Markov Operators

Content Provider	Springer Nature Link
Author	Makarov, I. I.
Copyright Year	2000
Abstract	Let (X,Σ,µ) be a probability space. An operator P : L $^{1}$(X,Σ,µ) ↓ L $^{1}$(X,Σ,µ) is called a Markov operator if it satisfies the following conditions:(1) $$P1 = 1$$ ;(2) $$\forall f \in L^1 (X,\sum ,\mu ),{\text{ }}f \geqslant 0 \Rightarrow Pf \geqslant 0$$ ;(3) $$\int\limits_X {Pf{\text{ d}}\mu } = \int\limits_X {f{\text{ d}}\mu } $$ . The purpose of this paper is to extend the notion of entropy to the class of Markov operators. The relationship between the Kolmogorov–Sinai entropy and new defined one will be examined.
Starting Page	1
Ending Page	11
Page Count	11
File Format	PDF
ISSN	10792724
Journal	Journal of Dynamical and Control Systems
Volume Number	6
Issue Number	1
e-ISSN	15738698
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2000-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Analysis Applications of Mathematics Systems Theory, Control Calculus of Variations and Optimal Control Optimization
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Algebra and Number Theory Numerical Analysis

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Dynamical Entropy for Markov Operators