Geodesic
Asymptotic behavior of large deviation probabilities for two weighted sums of random variables
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider two weighted sums of independent identically distributed non-lattice variables. We assume that the mean of the first sum is less than the mean of the second sum and consider the probability of the rare event that the first sum is greater than the second one. We assume the Cramer's condition for the summands. Under some additional assumptions we study the asymptotical behaviour of the probability above. The results are applied to the gladiator model introduced by K. Kaminsky, E. Luks and P. Nelson. 
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M. A. Khodiakova. Asymptotic behavior of large deviation probabilities for two weighted sums of random variables. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2024), pp. 3-13. http://geodesic.mathdoc.fr/item/VMUMM_2024_4_a0/

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