In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear...

In stochastic optimization models the underlying probability measure must be very often replaced by its approximations. This leads to the investigation of the stability of such models with respect to changes in the probability measure. In this context, special attention is paid to recourse...

<p><span style="font-size: 11.000000pt; font-family: 'CMR10';">In this paper, we aim to explore the speed of convergence of the Wasserstein distance between stable cumulative distribution functions and their empirical counterparts. The theoretical results are compared with the results provided by simulations. The need to use simulations is explained by the...</span></p>

The subject of this paper is the estimation of a probability measure on Rd from the data observed with an additive noise, under the Wasserstein metric of order p (with p≥1). We assume that the distribution of the errors is known and belongs to a class of supersmooth distributions, and we give...

We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in...