Structure of mixing and category of complete mixing for stochastic operators

• Autorzy: Anzelm Iwanik , Ryszard Rębowski
• Języki publikacji: EN

Abstrakty

EN

Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak compactness. Finally, it is shown that most stochastic operators are completely mixing and that the same holds for convolution stochastic operators on l.c.a. groups.

Kategorie tematyczne

• 47A35: Ergodic theory
• 60J05: Discrete-time Markov processes on general state spaces
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 3
• Strony: 233-242

Daty

wydano

1992

otrzymano

1990-08-01

poprawiono

1991-11-04

Twórcy

autor

Anzelm Iwanik

• Institute of Mathematics, Technical University of Wrocław Wybrzeże, Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Ryszard Rębowski

• Institute of Mathematics, Technical University of Wrocław Wybrzeże, Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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