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Abstrakty
The strong laws of large numbers for random permanents of increasing order are derived. The method of proofs relies on the martingale decomposition of a random permanent function similar to the one known for U-statistics.
Czasopismo
Rocznik
Tom
Strony
201--209
Opis fizyczny
Biblogr. 8 poz.
Twórcy
autor
- Department of Mathematics, University of Louisville, Kentucky, USA
autor
- Department of Mathematics and Information Science, Warsaw University of Technology, Poland
Bibliografia
- [1] Y. S. Chow and H. Teicher, Probability Theory. Independence, Interchangeability, Martingales,, third edition, Springer, New York 1997.
- [2] V. L. Girko, Theory of Random Determinants, Mathematics and Its Applications (Soviet Series), Vol. 45, Kluwer Academic Publishers Group, Dordrecht 1990. Translated from Russian.
- [3] G. Halász and G. J. Szèkely, On the elementary symmetric polynomials of independent random variables, Acta Math. Acad. Sci. Hungar. 28 (1976), pp. 397-400.
- [4] G. Rempała and A. K. Gupta, Almost sure behavior of elementary symmetric polynomials, Random Oper. Stochastic Equations 8 (2000), pp. 39-50.
- [5] G. Rempała and J. Wesołowski, Limiting behavior of random permanents, Statist. Probab. Lett. 45 (1999), pp. 149-158.
- [6] G. Rempała and J. Wesołowski, Central limit theorems for random permanents with correlation structure, J. Theoret. Probab. 14 (2001), pp. 1097-1110.
- [7] G. J. Szèkely, A limit theorem for elementary symmetric polynomials of independent random variables, Z. Wahrsch. verw. Gebiete 59 (1982), pp. 355-359.
- [8] A. J. van Es and R. Helmers, Elementary symmetric polynomials of increasing order, Probab. Theory Related Fields 80 (1988), pp. 21-35.
Typ dokumentu
Bibliografia
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