Consider a probability measure μ supported by a regular geodesic ball in a manifold. For any p≥1 we define a stochastic algorithm which converges almost surely to the p-mean ep of μ. Assuming furthermore that the functional to minimize is regular around ep, we prove that a natural...

Let η=(η(t))t∈T be a sample continuous max-infinitely random field on a locally compact metric space T. For a closed subset S⊂T, we denote by ηS the restriction of η to S. We consider β(S1,S2), the absolute regularity coefficient between ηS1 and ηS2, where S1,S2 are two disjoint...

We consider weighted random balls in distributed according to a random Poisson measure with heavy-tailed intensity and study the asymptotic behavior of the total weight of some configurations in while we perform a zooming operation. The resulting procedure is very rich and several regimes appear...

We prove a stable version of the Lindeberg–Feller theorem and apply this result to an approximation of stable processes that are represented by stochastic integrals.

We consider the Glivenko-Cantelli-type asymptotic behaviour of the empirical generalized Lorenz curves based on random variables forming a stationary ergodic sequence with deterministic noise. As a consequence of these results, we obtain a description of the set of limiting curves of the...

We consider the invariance principle without the classical condition of asymptotic negligibility of individual terms. More precisely, let r.v.'s {[xi]nj} and {[eta]nj} be such that and the r.v.'s {[eta]nj} are normal. We set Let Xn(t) and Yn(t) be continuous piecewise linear (or polygonal)...