An extension of a Meyer's theorem
An extension of an inequality due to Stein and Lepingle
Hardy spaces consisting of adapted function sequences and generated by the q-variation and by the conditional q-variation are considered. Their dual spaces are characterized and an inequality due to Stein and Lepingle is extended.
An extension of Mineka's coupling inequality.
An extension of the Clark-Ocone formula.
An extension theorem to rough paths
An extremal problem related to probability.
An extreme Markovian-evolutionary (EME) sequence.
The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.
An Improved General Stochastic Inequality
An improved version of a theorem concerning finite row-column exchangeable arrays
We improve a result of Bassan and Scarsini (1998) concerning necessary conditions for finite and infinite extendibility of a finite row-column exchangeable array, and provide a simpler proof for the result.
An inequality for the asymmetry of distributions and a Berry-Esseen theorem for random summation.
An inequality for the predictable projection of an adapted process
An infinite dimensional central limit theorem for correlated martingales
An integral representation for the Hellinger distance.
An integral representation of randomized probabilities and its applications
An integral test for the transience of a brownian path with limited local time
We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function f(t), t≥0, consider the measures μt obtained by conditioning a brownian path so that Ls≤f(s), for all s≤t, where Ls is the local time spent at the origin by time s. It is shown that the measures μt are tight, and that any weak limit of μt as t→∞ is transient provided that t−3/2f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems....
An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions.
An interpolation problem for multivariate stationary sequences
Let and be stationarily cross-correlated multivariate stationary sequences. Assume that all values of and all but one values of are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].
An invariance principle for Azéma martingales
An Invariance Principle for Progressively Truncated Likelihood Ratio Statistics.
An invariance principle in for non stationary -mixing sequences
Invariance principle in is studied using signed random measures. This approach to the problem uses an explicit isometry between and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a version of the invariance principle in the case of -mixing random variables. Our result is not available in the -setting.