CENTRAL LIMIT THEOREM OF MIXED TYPE FOR TRANSFORMATIONS WITH QUASI-COMPACT PERRON-FROBENIUS OPERATORS

• IKEDA Takuya

  Department of Mathematics Graduate School of Science Osaka University

• MORITA Takehiko

  Department of Mathematics Graduate School of Science Osaka University

抄録

We consider a nonsingular transformation whose Perron-Frobenius operator is quasi-compact on an appropriate Banach algebra. We establish the central limit theorem of mixed type with a nice convergence rate for a real-valued observable in the Banach algebra. As an application, we show that generalized piecewise expanding maps on the unit interval with Hölder continuous derivatives and the Banach algebra of Lebesgue integrable functions with a version of bounded p-variation satisfy our conditions if p is not smaller than the reciprocal of the Hölder exponent of the derivatives.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 71 (1), 31-64, 2017

  九州大学大学院数理学研究院

キーワード

• central limit theorem of mixed type
• perturbed Perron-Frobenius operator

詳細情報

• CRID: 1390001205228510336
• NII論文ID: 130005666230
• DOI: 10.2206/kyushujm.71.31
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/71/1/71_31/_pdf
• 本文言語コード: en
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