This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating...

Let be i.i.d. -valued random variables. We prove partial moderate deviation principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.

Let (Xi,Ui) be i.i.d., Xi real valued and Ui vector valued, bounded random variables or governed by a finite state Markov chain. Assuming that E[X]<0 and P(X> 0) 0, central limit theorems are derived for [Sigma]iUi on segments conditioned that [Sigma]iXi is increasingly high, going to +[infinity]. While...</0>

We show that the large deviation principle with respect to the weak topology holds for the empirical measure of any stationary continuous-time Gaussian process with continuous vanishing at infinity spectral density. We also point out that large deviation principle might fail in both continuous...

For {Xi}i = 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t = 0}n = 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t = 0}n = 1,...

The large deviation principle is known to hold for the empirical measures (occupation times) of Polish space valued random variables and for the empirical means of Banach space valued random variables under Markov dependence or mixing conditions, and subject to the appropriate exponential tail...

The exact lower tail of Gaussian seminorms are evaluated, using a refinement of the techniques presented in Mayer-Wolf and Zeitouni (1993).

If for a 'permissible' family of functions and an i.i.d. process {Xi}[infinity]i=0, with probability one, then the same holds for away absolutely regular (weakly Bernoulli) process having the same marginal distribution. In particular, for any class of sets having finite V-C dimension and any...

Consider a sequence of m deterministic points in ##R##d, and consider the empirical measure of a random sample (without replacements) of size n = n(m). We prove the large deviation principle and compute the resulting rate function for the latter empirical measure under the assumptions that the...