Cauchy-Stieltjes Families with Polynomial Variance Functions and Generalized Orthogonality

• Autorzy: Bryc Włodzimierz , Fakhfakh Raouf , Młotkowski Wojciech

Identyfikatory

DOI

10.19195/0208-4147.39.2.1

• Języki publikacji: EN

Abstrakty

EN

This paper studies variance functions of Cauchy-Stieltjes Kernel (CSK) families generated by compactly supported centered probability measures. We describe several operations that allow us to construct additional variance functions from known ones. We construct a class of examples which exhausts all cubic variance functions, and provide examples of polynomial variance functions of arbitrary degree. We also relate CSK families with polynomial variance functions to generalized orthogonality. Our main results are stated solely in terms of classical probability; some proofs rely on analytic machinery of free probability.

Słowa kluczowe

EN

kernel families; generalized orthogonality; R-transform; S-transform; Fuss-Catalan numbers; variance functions; free additive convolution; free multiplicative convolution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 237--258
• Opis fizyczny: Bibliogr. 46 poz.

Twórcy

autor

Bryc Włodzimierz

• Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA

autor

Fakhfakh Raouf

• Mathematics Department, College of Science and Arts in Gurayat, Jouf University, Gurayat, Saudi Arabia, and Laboratory of Probability and Statistics, Sfax University, Sfax, Tunisia

autor

Młotkowski Wojciech

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).