Σ-finite invariant densities for eventually conservative Markov operators

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

We establish equivalent conditions for the existence of an integrable or locally integrable fixed point for a Markov operator with the maximal support. Maximal support means that almost all initial points will concentrate on the support of the invariant density under the iteration of the process. One of the equivalent conditions for the existence of a locally integrable fixed point is weak almost periodicity of the jump operator with respect to some sweep-out set. This result includes the case of the existence of an absolutely continuous σ-finite invariant measure when we consider a nonsingular transformation on a probability space. Weak almost periodicity implies the Jacobs-Deleeuw-Glicksberg splitting and we show that constrictive Markov operators which guarantee the spectral decomposition are typical weakly almost periodic operators.

本文言語英語
ページ(範囲)2641-2669
ページ数29
ジャーナルDiscrete and Continuous Dynamical Systems- Series A
40
5
DOI
出版ステータス出版済み - 2020
外部発表はい

All Science Journal Classification (ASJC) codes

  • 分析
  • 離散数学と組合せ数学
  • 応用数学

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