Let {Xi(t),t≥0},1≤i≤n be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants u,T, define the set of conjunctions C[0,T],u≔{t∈[0,T]:min1≤i≤nXi(t)≥u}. Motivated by some applications in brain...

In this paper we discuss the link between Archimedean copulas and L1 Dirichlet distributions for both finite and infinite dimensions. With motivation from the recent papers Weng et al. (2009) and Albrecher et al. (2011) we apply our results to certain ruin problems.

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in...

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability and the conditional probability , for x,y large.

The class of Dirichlet random vectors is central in numerous probabilistic and statistical applications. The main result of this paper derives the exact tail asymptotics of the aggregated risk of powers of Dirichlet random vectors when the radial component has df in the Gumbel or the Weibull...