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2 Zaigraev A.

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Multivariate large deviations for sums of i.i.d. random vectors with compactly supported distribution

Zaigraev A.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 2

315--335

The sums of i.i.d. random vectors with compactly supported and absolutely continuous distribution are considered. Under some conditions the strong form of the local limit theorem for large deviations is proved. In passing the asymptotic behaviour of the moment generating function as well as possible non-degenerate limit laws for the natural exponential family of distributions are established.

Multivariate large deviations with stable limit laws

Zaigraev A.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

323--335

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.