On the range of the simple random walk bridge on groups.
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 Lev́y processes with no positive jumps conditioned to stay positive.
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 rate of strong mixing in stationary Gaussian random fields
Rosenblatt showed that a stationary Gaussian random field is strongly mixing if it has a positive, continuous spectral density. In this article, spectral criteria are given for the rate of strong mixing in such a field.
On the ratio of Pearson type VII and Bessel random variables.
On the Ray topology
On the reconstruction of a killed Markov process
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 refined Heisenberg-Weyl type inequality.
On the regularity of many-particle dynamical systems perturbed by white noise.
On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model
We study the pathwise regularity of the map φ↦I(φ)=∫0T〈φ(Xt), dXt〉, where φ is a vector function on ℝd belonging to some Banach space V, X is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of V will be called stochastic current. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture...
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On the relation between Gaussian measures and convolution semigroups of local type.
On the relationship between Menger spaces and Wald spaces