Let Xt be the pathwise solution of a diffusion driven by a fractional Brownian motion with Hurst constant H1/2 and diffusion coefficient [sigma](t,x). Consider the successive increments of this solution, [Delta]Xi=Xi/n-X(i-1)/n. Using a cylinder approximation for the solution Xt, our main result...

Controlled branching processes (CBP) with a random control function provide a useful way to model generation sizes in population dynamics studies, where control on the growth of the population size is necessary at each generation. An important special case of this process is the well known...

We give a new and comparably short proof of Gittins' index theorem for dynamic allocation problems of the multi-armed bandit type in continuous time under minimal assumptions. This proof gives a complete characterization of optimal allocation strategies as those policies which follow the current...

The paper develops a limit theory for the quadratic form Qn,X in linear random variables X1,...,Xn which can be used to derive the asymptotic normality of various semiparametric, kernel, window and other estimators converging at a rate which is not necessarily n1/2. The theory covers practically...

Let (W,[mu],H) be an abstract Wiener space and assume that Y is a signal of the form Y=X+w, where X is an H-valued random variable, w is the generic element of W. Under the hypothesis of independence of w and X, we show that the quadratic estimate of X, denoted by , is of the form [backward...

In this paper one specifies the ergodic behavior of the 2D-stochastic Navier-Stokes equation by giving a Large Deviation Principle for the occupation measure for large time. It describes the exact rate of exponential convergence. The considered random force is non-degenerate and compatible with...

We consider the problem of giving explicit spectral bounds for time inhomogeneous Markov chains on a finite state space. We give bounds that apply when there exists a probability [pi] such that each of the different steps corresponds to a nice ergodic Markov kernel with stationary measure [pi]....

We consider the deviation function in the ergodic theorem for an ergodic diffusion process (yt) where [phi] is some function, m([phi]) is the integral of [phi] with respect to the ergodic distribution of (yt). We prove a concentration inequality for [Delta]T([phi]) which is uniform with respect...

We prove a central limit theorem for the d-dimensional distribution function of a class of stationary sequences. The conditions are expressed in terms of some coefficients which measure the dependence between a given [sigma]-algebra and indicators of quadrants. These coefficients are weaker than...

We consider first passage times for piecewise exponential Markov processes that may be viewed as Ornstein-Uhlenbeck processes driven by compound Poisson processes. We allow for two-sided jumps and as a main result we derive the joint Laplace transform of the first passage time of a lower level...