A note on invariant sets

• Autorzy: Schilling R. L.
• Języki publikacji: EN

Abstrakty

EN

A measurable set A is invariant with respect to a not necessarily symmetric sub-Markovian operator T on L^p (X, m) if T1_A ≤ 1_A, and strongly invariant if T1_A = 1_A. We show that these definitions accommodate many of the usual definitions of invariance, e.g., those used in Dirichlet form theory, ergodic theory or for stochastic processes. In finite measure spaces or if T^∗ is sub-Markovian and recurrent, the notions of invariance and strong invariance coincide. We also show that for certain analytic semigroups of sub-Markovian operators, (strongly) invariant sets are already determined by a single operator, T₁.

Słowa kluczowe

EN

invariant set; sub-Markov operator; recurrence; transience; fractional power; analytic semigroup

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 1
• Strony: 47--66
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Schilling R. L.

• Department of Mathematics, University of Sussex, Brighton BN1 9RF, U.K.

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