Domain of attraction of Gaussian probability operators in quantum limit theory

• Autorzy: Lubnauer K. , Łuczak A.
• Języki publikacji: EN

Abstrakty

EN

We characterise the class of probability operators belonging to the domain of attraction of Gaussian limits in the setup which is a slight generalisation of Urbanik’s scheme of noncommutative probability limit theorems.

Słowa kluczowe

EN

probability operators; quantum limit theorem; domain of attraction

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 1
• Strony: 141--152
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Lubnauer K.

• Faculty of Mathematics and Computer Science, Łódź University, ul. S. Banacha 22, 90-238 Łódź, Poland

autor

Łuczak A.

• Faculty of Mathematics and Computer Science, Łódź University, ul. S. Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] C. D. Cushen and R. L. Hudson, A quantum mechanic central limit theorem, J. Appl. Probab. 8 (1971), pp. 454-469.
• [2] W. Feller, An Introduction to Probability Theory, Vol. II (in Polish), PWN, Warszawa 1978.
• [3] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam 1982.
• [4] K. Lubnauer, Operator-stable quantum probability operators, J. Math. Sci. 106 (2001), pp. 2713-2718.
• [5] K. Lubnauer, Quantum limit theorems, Studia Math. 164 (2004), pp. 103-120.
• [6] K. Urbanik, Non-commutative probability limit theorems, Studia Math. 78 (1984), pp. 59-75.