Mathematics

Asymptotic behavior of large deviation probabilities for two weighted sums of random variables

M. A. Khodiakova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: large deviations, weighted sums, limit theorems, integro-local theorems, gladiator game.

UDC: 511

Received: 10.05.2023

DOI: 10.55959/MSU0579-9368-1-65-4-1

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2024, 79:4, 147–158

Bibliographic databases:

•