The superposition Markov chain : finite occupancy with coupling, and the asymptotics thereof

• Autorzy: Günther B.
• Języki publikacji: EN

Abstrakty

EN

Picking up a lottery example by Markov we analyze a variant of the finite occupancy problem that assumes complete symmetry among the target cells but drops the customary assumptions about independence. Assuming that the distribution of the number of non-empty cells approaches a non-trivial asymptotic limit for large state space sizes the limit time evolution is studied.

Słowa kluczowe

EN

random allocation; weak limit theorems; finite Markov chains; Stirling polynomials

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 1
• Strony: 103--120
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Günther B.

• DB-Systel GmbH, Helpertseestraße 21, 63165 Mühlheim, Germany

Bibliografia

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• [2] B. Günther, On the probability distribution of superimposed random codes, IEEE Trans. Inform. Theory 54 (7) (2008), pp. 3206-3210. DOI 10.1109/TIT.2008.924658.
• [3] C. Jordan, Calculus of Finite Differences, AMS Chelsea, 1965. Reprint 1979.
• [4] V. F. Kolchin, B. A. Sevast’yanov and V. P. Christyakov, Random Allocations, Scripta Series in Mathematics, Wiley, 1978.
• [5] S. Kotz and N. Balakrishnan, Advances in urn models during the past two decades, in: Advances in Combinatorial Methods and Applications to Probability and Statistics, N. Balakrishnan (Ed.), Birkhäuser, 1997, pp. 203-257.
• [6] P. A. MacMahon, Combinatory Analysis, Phoenix Editions, Dover 2004. Reprint Vol. I (1915), Vol. II (1916) and Intro (1920).
• [7] A. A. Markoff, Wahrscheinlichkeitsrechnung, Teubner, 1912.
• [8] S. M. Mirakhmedov, Asymptotic normality associated with generalized occupancy problems, Statist. Probab. Lett. 77 (15) (2007), pp. 1549-1558.
• [9] C. S. Roberts, Partial-match retrieval via the method of superimposed codes, Proceedings of the IEEE 67 (12) (1979), pp. 1624-1642.
• [10] S. Roman, The Umbral Calculus, Dover 2005.