大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

A generalisation of a result of Mark Kac (Ann.Maths. 47 (1946))

Freddy Delbaen (ETH Zurich)

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大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第87回 (理学研究科確率論セミナー主催)

A generalisation of a result of Mark Kac (Ann.Maths. 47 (1946))

Freddy Delbaen (ETH Zurich)

In 1946 Mark Kac proved that for a centred Hoelder continuous function $f$ defined on $[0,1]$ and extended periodically to the whole real line, the sequence $f(2^k t)$ satisfies a Central Limit Theorem. We extend the result to measurable $L^2$ functions satisfying a fast approximation property. The result naturally extends to similar functions defined on Bernoulli shifts.

Joint work with Emma Hovhannisyan and Ashkan Nikeghbali (both from the University of Zurich).