Une transformation de Cramer sur le dual de
Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach...
Uniform exponential bound for the normalized empirical process
Upper large deviations for maximal flows through a tilted cylinder
We consider the standard first passage percolation model in ℤd for d ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to n and whose height is h(n) for a certain height function h. We denote this maximal flow by τn (respectively φn). We emphasize the fact that the cylinder may be tilted. We look at the probability that these flows, rescaled by the surface...
Upper tails of self-intersection local times of random walks: survey of proof techniques
The asymptotics of the probability that the self-intersection local time of a random walk on exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated...
Varadhan's theorem for capacities
Varadhan's integration theorem, one of the corner stones of large-deviation theory, is generalized to the context of capacities. The theorem appears valid for any integral that obeys four linearity properties. We introduce a collection of integrals that have these properties. Of one of them, known as the Choquet integral, some continuity properties are established as well.
Variational representations for continuous time processes
A variational formula for positive functionals of a Poisson random measure and brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.
Viscosity solutions of two classes of coupled Hamilton-Jacobi-Bellman equations.
Voiculescu’s Entropy and Potential Theory
We give a new proof, relying on polynomial inequalities and some aspects of potential theory, of large deviation results for ensembles of random hermitian matrices.
Wave propagation in a lattice KPP equation in random media.
Yule process sample path asymptotics.
Асимптотическая эффективность по Бахадуру интегральных критериев симметрии
Асимптотическое поведение частичной суммы ряда из вероятностей больших уклонений
Большие уклонения в линейной модели с мешающими параметрами
Большие уклонения в пространстве C(0,1) для сумм, заданных на конечной цепи Маркова
Большие уклонения в пространстве траекторий для последовательностей и процессов со стационарными приращениями
Большие уклонения для выборочных квантилей
Большие уклонения и асимптотическая эффективность статистик интегрального типа. I
Большие уклонения и асимптотическая эффективность статистик интегрального типа. II
Большие уклонения и бахадуровская эффективность статистики Хмаладзе-Аки