An extension of Billingsley’s uniform boundedness theorem to higher-dimensional -processes
An extension of the Borel lemma
An extremal problem arising in soil erosion modeling
An extreme-value analysis of the LIL for Brownian motion.
An Improved General Stochastic Inequality
An individual ergodic theorem for random fuzzy sets.
An inequality for the asymmetry of distributions and a Berry-Esseen theorem for random summation.
An inequality for the distribution of a sum of certain Banach space valued random variables
An infinite dimensional central limit theorem for correlated martingales
An integral representation for the Hellinger distance.
An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions.
An invariance principle for Azéma martingales
An invariance principle for Markov processes and brownian particles with singular interaction
An Invariance Principle for Progressively Truncated Likelihood Ratio Statistics.
An Invariance Principle for Reduced U-Statistics.
An invariance principle for the law of the iterated logarithm for some Markov chains
Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
An Invariance Principle for U-Statistics in Simple Random Sampling without Replacement.
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.
An invariance principle for LPQD random variables.
An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm...