On the number of local extrema in a sequence of independent random variables
On the order of growth of convergent series of independent random variables.
On the Poisson approximation of the binomial distribution.
On the Poisson approximation to the negative hypergeometric distribution.
On the Power of Nonparametric Changepoint-Tests.
On the rate of approximation in the random sum CLT for dependent variables
Capital and lower-case approximations of the expected value of a class of smooth functions of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).
On the rate of convergence in the central limit theorem
On the rate of convergence in the central limit theorem for martingale difference sequences
On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...
On the rate of convergence of bootstrapped means in a Banach space.
On the rate of growth of subordinators with slowly varying Laplace exponent
On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the remainder term of the de Moivre-Laplace formula.
On the sample path behavior of the first passage time process of a brownian motion with drift
On the sequence of integer parts of a good sequence for the ergodic theorem
If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
On the small deviation problem for some iterated processes.
On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations
In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.
On the speed of coming down from infinity for -coalescent processes.
On the sphericity of scaling limits of random planar quadrangulations.