A nonuniform bound for the approximation of Poisson binomial by Poisson distribution.
A non-uniform bound for translated Poisson approximation.
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 Hájek's Theory of Rejective Sampling.
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 Sampford-Durbin sampling
A note on the asymptotic independence of maximum and minimum of stationary sequences with extremal index
A note on the invariance principle of the product of sums of random variables.
A note on the k-th distance random variables
A note on the martingale central limit theorem
A penalized bandit algorithm.
A probabilistic approach to the asymptotics of the length of the longest alternating subsequence.
A probabilistic description of the three theorems of Hardy.
A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree.
A proof of a non-commutative central limit theorem by the Lindeberg method.
A Proof of Asymptotic Normality for some VARX Models.
A quenched weak invariance principle
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.