Generalized t-transformations of probability measures and deformed convolutions

• Autorzy: Krystek A. , Yoshida H.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the generalized (two-parameterized) t-transformations on probability measures are introduced, in which the t-transformation of Bożejko and Wysoczański can be obtained as the special case, and the associated deformed convolutions are also investigated. We see that the generalized t-deformed free convolution can be realized as the conditionally free convolution of Bożejko, Leinert, and Speicher. We also study another special case of the generalized t-deformed free convolution, which is called the τ-free convolution, that gives an interpolation between the free and the Fermi convolutions.

Słowa kluczowe

EN

convolution; conditionally free; moment-cumulant formula

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 1
• Strony: 97--119
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Krystek A.

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

autor

Yoshida H.

• Department of Information Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo, Tokyo, 112-8610 Japan

Bibliografia

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• [3] M. Bożejko, M. Leinert, and R. Speicher, Convolution and limit theorems for conditionally free random variables, Pacific J. Math. 175 (1996), pp. 357-388.
• [4] M. Bożejko and J. Wysoczański, New examples of convolution and non-commutative central limit theorems, Banach Center Publ. 43 (1998), pp. 95-103.
• [5] M. Bożejko and J. Wysoczański, Remarks on t-transformations of measures and convolutions, Ann. Inst. H. Poincaré Probab. Statist. 37 (2001), pp. 737-761.
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• [7] F. Oravecz, Fermi convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), pp. 235-242.
• [8] N. Saitoh and H. Yoshida, The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory, Probab. Math. Statist. 21 (2001), pp. 159-170.
• [9] R. Speicher, A new example of 'Independence' and 'White Noise’: Probab. Theory Related Fields 84 (1990), pp. 141-159.
• [10] H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand Company, New York 1948.