The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: i) tension is constant with respect to time, and ii) tension v...

We introduce a flow of maps from a compact surface of arbitrary genus to an arbitrary Riemannian manifold which has elements in common with both the harmonic map flow and the mean curvature flow, but is more effective at finding minimal surfaces. In the genus 0 case, our flow is just the harmonic map flow, and it tries to find branched minimal 2-spheres as in Sacks-Uhlenbeck [13] and Struwe [16...

An elementary approach is used to derive a Bayes-type formula, extending the Kallianpur–Striebel formula for the nonlinear filters associated with the Gaussian noise processes. In the particular cases of certain Gaussian processes, recent results of Kunita and of Le Breton on fractional Brownian motion are derived. We also use the classical approximation of the Brownian motion by the Ornstein–U...

Abstract: We consider an Ornstein-Uhlenbeck process with values in Rn driven by a Lévy process (Zt) taking values in R d with d possibly smaller than n. The Lévy noise can have a degenerate or even vanishing Gaussian component. Under a controllability rank condition and a mild assumption on the Lévy measure of (Zt), we prove that the law of the Ornstein-Uhlenbeck process at any time t > 0 has a...

We prove that the density fluctuations for a zero-range process evolving on the d-dimensional supercritical percolation cluster, with d ≥ 3, are given by a generalized Ornstein-Uhlenbeck process in the space of distributions S (R).

We consider solutions of Burgers’ equation with linear or quadratic external potential and stationary random initial conditions of Ornstein–Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half. A.M.S. Classification: 60F10, 60G15, 60J65

We suggest a certain statistical interpretation for the entropy produced in driven thermodynamic processes. The exponential function of the irreversible entropy re-weights the probability of the standard Ornstein-Uhlenbeck-type thermodynamic fluctuations. ∗E-mail: [email protected]