MULTIVARIATE LARGE DEVIATIONS WITH STABLE LIMIT LAWS

Abstract: The large deviation problem for sums of i.i.d. random vectors is considered. It is
assumed that the underlying distribution is absolutely continuous and its density is of regular
variation. An asymptotic expression for the probability of large deviations is established in
the case of a non-normal stable limit law. The role of the maximal summand is also
emphasized.

1991 AMS Mathematics Subject Classification: Primary 60F10; Secondary
60G50.

Key words and phrases: sums of i.i.d. random vectors, local limit theorem, regular
variation, maximal summand.