A nonergodic version of Gordin's CLT for integrable stationary processes
A non-Skorokhod topology on the Skorokhod space.
A nonuniform bound for the approximation of Poisson binomial by Poisson distribution.
A non-uniform bound for translated Poisson approximation.
A Note Invariance Principles for v. Mises'-Statistics.
A note on almost sure central limit theorem in the joint version for the maxima and sums.
A note on almost sure convergence and convergence in measure
The present article studies the conditions under which the almost everywhere convergence and the convergence in measure coincide. An application in the statistical estimation theory is outlined as well.
A note on convergence of weighted sums of random variables.
A note on Cramer's theorem
A Note on Hájek's Theory of Rejective Sampling.
A note on large deviations for Wiener chaos
A note on Poisson approximation.
We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall.It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate conditions, such that p = 1/n Σipi → 0, np → ∞, np2 → 0, then the total variation distance between X1+...+Xn...
A note on Poisson approximation by w-functions
One more method of Poisson approximation is presented and illustrated with examples concerning binomial, negative binomial and hypergeometric distributions.
A note on quenched moderate deviations for Sinai’s random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is .
A note on quenched moderate deviations for Sinai's random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than ta (0<a<1) from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.
A note on random walk in random scenery
A note on reinsurance contracts with multiple reinstatements
A note on Sampford-Durbin sampling
A note on strong convergence of sums of dependent random variables.
A note on strong laws of large numbers for dependent random sets and fuzzy random sets.