Probability on matrix-cone hypergroups: limit theorems and structural properties

• Autorzy: Hazod W.
• Języki publikacji: EN

Abstrakty

EN

Recent investigations of M. Rösler [13] and M. Voit [17] provide examples of hypergroups with properties similar to the group-or vector space case and with a sufficiently rich structure of automorphisms, providing thus tools to investigate the limit theory of normalized random walks and the structure of the corresponding limit, laws. The investigations are parallel to corresponding investigations for vector spaces and simply connected nilpotent Lie groups.

Słowa kluczowe

EN

stability; semistability; Wishart distribution; Gaussian distribution; hypergroup; self-decomposability

PL

stateczność; pół-stateczność; rozkład Wisharta; rozkład Gaussiana

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2009
• Tom: Vol. 15, nr 2
• Strony: 205--245
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Hazod W.

• Faculty of Mathematics Technische Universität Dortmund,

Bibliografia

• [1] Barndorf-Nielsen, O., Pedersen, J., Sato, K., Multivariate subordination, self-decomposability and stability, Adv. in Appl. Probab. 33 (2001), 160-187.
• [2] Bloom, W., Heyer, H., Harmonic Analysis of Probability Measures on Hypergroups. Walter de Gruyter, Berlin-New York, 1995.
• [3] Hazod, W., On normalizers and centralizers of compact Lie groups. Applications to structural probability theory, Probab. Math. Statist. 23 (2003), 39-60.
• [4] Hazod, W., Normalizers and centralizers of compact matrix groups. An elementary approach, Linear Algebra Appl. 410 (2005), 96-111.
• [5] Hazod, W., Siebert, E., Stable Probability Measures on Euclidean Spaces and on Locally Compact Groups. Structural Properties and Limit Theorems, Math. Appl. 531, Kluwer Acad. Publ., Dordrecht, 2001.
• [6] Hewitt, E., Ross, K. A., Abstract Harmonic Analysis, Springer, Berlin-Heidelberg-New York, 1963.
• [7] Heyer, H., Probability Measures on-Locally Compact Groups, Springer, Berlin-Heidelberg-New York, 1977.
• [8] Jewett, R. I., Spaces with an abstract convolution of measures, Adv. Math. 18 (1975), 1-101.
• [9] Jurek, Z., Mason, D., Operator Limit Distributions in Probability Theory, J. Wiley & Sons, Inc., New York, 1993.
• [10] Meerschaert, M. M., Scheffler, H-P., Limit Theorems for Sums of Independent Random Vectors. Heavy Tails in Theory and Praxis, J. Wiley & Sons, Inc., New York, 2001.
• [11] Menges, S., Stetige Faltungshalbgruppen und Grenzwertsätze auf Hypergruppen, Dissertation, Universität Dortmund, Dortmund, 2003.
• [12] Menges, S., Functional limit theorems for probability measures on hypergroups, Probab. Math. Statist. 25 (2005), 155-171.
• [13] Rösler, M., Bessel convolutions on matrix cones. Compos. Math. 143 (2007), 749-779.
• [14] Sato, K., Lévy Processes and Infinitely divisible Distributions, Cambridge Univ. Press, Cambridge, 1999.
• [15] Scheffler, H. P., Zeuner, H. M., Domains of attraction on Sturm-Liouville hypergroups of polynomial growth, J. Appl. Anal. 5 (1999), 153-170.
• [16] Voit, M., Positive and negative definite functions on the dual space of a commutative hypergroup, Analysis 9 (1989), 371-387.
• [17] Voit, M., Bessel convolutions on matrix cones: Algebraic properties and random, walks. J. Theoret. Probab. 22 (2009), 741-771.
• [18] Zeuner, H. M., Domains of attraction with inner norming on Sturm-Liouville hypergroups, J. Appl. Anal. 2 (1995), 213-221.
• [19] Zeuner, H. M., Kolmogorov's three series theorem on one-dimensional hypergroups. Contemp. Math. 183 (1995), 435-441.