On the convergence of sequences of iterates of random-valued functions.
On the convergence of sequences of iterates of random-valued vector functions
Given a probability space (Ω,,P) and a subset X of a normed space we consider functions f:X × Ω → X and investigate the speed of convergence of the sequence (fⁿ(x,·)) of the iterates defined by f¹(x,ω ) = f(x,ω₁), .
On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.
On the Convergence of the Critical Values of Uniformly Most Powerful Unbiased Tests for Two-Sided Hypotheses.
On the convergence of the ensemble Kalman filter
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and bounds on the ensemble then give convergence.
On the difference between the product and the convolution product of distribution functions.
On the discretization in time of parabolic stochastic partial differential equations
We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are not able in this case to compute a pathwise order of the approximation, we introduce the weaker notion...
On the discretization in time of parabolic stochastic partial differential equations
We first generalize, in an abstract framework, results on the order of convergence of a semi-discretization in time by an implicit Euler scheme of a stochastic parabolic equation. In this part, all the coefficients are globally Lipchitz. The case when the nonlinearity is only locally Lipchitz is then treated. For the sake of simplicity, we restrict our attention to the Burgers equation. We are not able in this case to compute a pathwise order of the approximation, we introduce the weaker notion...
On the distribution density of the supremum of a random walk in the subexponential case.
On the distribution of random walk local time
On the distribution of the number of vertices in layers of random trees.
On the distributions of norms of weighted quantile processes
On the extremal behavior of sub-sampled solutions of stochastic difference equations.
On the Feller strong law of large numbers for fields of -valued random variables.
On the functional central limit theorem for stationary processes
On the increments of the principal value of Brownian local time.
On the invariance principle for non-uniformly expanding transformations of [0, 1].
On the -convergence for multidimensional arrays of random variables.
On the large deviations of a class of modulated additive processes
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn...
On the large deviations of a class of modulated additive processes
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn...