Let (µn : n = 0) be Borel probabilities on a metric space S such that µn - µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn - µn for all n and Xn - X0 in probability. By Skorohod's theorem, Skorohod...

Let (µn : n = 0) be Borel probabilities on a metric space S such that µn - µ0 weakly. Say that Skorohod representation holds if, on some probability space, there are S-valued random variables Xn satisfying Xn - µn for all n and Xn - X0 in probability. By Skorohod s theorem, Skorohod...

Let µn be a probability measure on the Borel sigma-field on D[0, 1] with respect to Skorohod distance, n = 0. Necessary and sufficient conditions for the following statement are provided. On some probability space, there are D[0, 1]-valued random variables Xn such that Xn tilde µn for all n =...

In this paper, a neutral stochastic partial differential equation is studied in real separable Hilbert spaces. The aim here is to introduce Yosida approximations for this class of equations and to show the convergence of the mild solutions of the Yosida approximating systems in the pth-mean...

In this paper, we deal with a class of time-homogeneous continuous-time Markov processes with transition probabilities bearing a nonparametric uncertainty. The uncertainty is modelled by considering perturbations of the transition probabilities within a proximity in Wasserstein distance. As a...

The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g. autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically normal with covariance structure depending on the second- and...

In this work, we propose to define Gaussian Processes indexed by multidimensional distributions. In the framework where the distributions can be modeled as i.i.d realizations of a measure on the set of distributions, we prove that the kernel defined as the quadratic distance between the...

IV regression in the context of a re-sampling is considered in the work. Comparatively, the contribution in the development is a structural identication in the IV model. The work also contains a multiplier-bootstrap justication.