A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
Štefan Šujan (1985)
Kybernetika
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Štefan Šujan (1985)
Kybernetika
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Ryotaro Sato (1983)
Studia Mathematica
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Gruher, Kate, Hines, Fred, Patel, Deepam, Silva, Cesar E., Waelder, Robert (2003)
The New York Journal of Mathematics [electronic only]
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Daniel W. Stroock (2010)
Colloquium Mathematicae
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Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves. ...
I. Assam, J. Woś (1990)
Studia Mathematica
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Jon Aaronson, Tom Meyerovitch (2008)
Colloquium Mathematicae
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We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.
Burgess Davis (1982)
Studia Mathematica
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David Kocheim, Roland Zweimüller (2011)
Studia Mathematica
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We study conservative ergodic infinite measure preserving transformations satisfying a compact regeneration property introduced by the second-named author in J. Anal. Math. 103 (2007). Assuming regular variation of the wandering rate, we clarify the asymptotic distributional behaviour of the random vector (Zₙ,Sₙ), where Zₙ and Sₙ are respectively the time of the last visit before time n to, and the occupation time of, a suitable set Y of finite measure.
Zbigniew Kowalski (1994)
Applicationes Mathematicae
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We consider the skew product transformation T(x,y)= (f(x), ) where f is an endomorphism of a Lebesgue space (X,A,p), e : X → S and is a family of Lasota-Yorke type maps of the unit interval into itself. We obtain conditions under which the ergodic properties of f imply the same properties for T. Consequently, we get the asymptotical stability of random perturbations of a single Lasota-Yorke type map. We apply this to some probabilistic model of the motion of cogged bits in the rotary...
Kakihara, Yûichirô (2003)
International Journal of Mathematics and Mathematical Sciences
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M. Courbage, D. Hamdan (2001)
Colloquium Mathematicae
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We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.
J. Choksi, M. Nadkarni (2000)
Colloquium Mathematicae
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It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...
Ryotaro Sato (1994)
Publicacions Matemàtiques
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Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averages Anf(x) = (n + 1)-d Σ0≤ni≤n f(T1 n1 T2 n2...