Invariant densities and mean ergodicity of Markov operators

Emel'yanov E.

ISRAEL JOURNAL OF MATHEMATICS, cilt.136, ss.373-379, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 136
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1007/bf02807206
  • Dergi Adı: ISRAEL JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.373-379
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

We prove that a, Markov operator T on L-1 has an invariant density if and only if there exists a density f that satisfies lim sup(n-->infinity) parallel toT(n) f-fparallel to < 2. Using this result, we show that a Frobenius-Perron operator P is mean ergodic if and only if there exists a density w such that lim sup(n-->infinity) parallel toP(n)f - wparallel to < 2 for every density f. Corresponding results hold for strongly continuous semigroups.