We give some easy methods to check sufficient conditions for the weak convergence of stochastic processes indexed by smooth functions. The main condition is a moment condition on the increments of the process. We apply this to empirical processes and U-processes in the independent identically...

This paper considers the a symptotic properties of an estimator of a parameter that generalizes the correlation coefficient to a class of nonlinear, non-Gaussian and positive time series models. The models considered are one step Markov chains whose innovations have an infinitely divisible...

We consider the Hopfield model with a finite number of randomly chosen patterns above and below the critical temperature and prove an almost sure conditional central limit theorem for the vector of overlap parameters. For this purpose we analyse the almost sure asymptotic behaviour of the...

We investigate the problem of edge estimation in a two-region image in the setting of a fixed design regression model. The edge estimation problem is equivalent to estimating one of the plateau sets where the regression function is constant, and we define a global set-valued estimator by finding...

We propose two general methods for coupling marked point processes (MPPs) on the real half-line that are explicitly formulated in terms of (canonical) compensators. These couplings are related to several results in the literature as compensator bounds for the total variation distance between two...

The problem of optimal fixed lag smoothing of a diffusion process, xt is to estimate xt - [tau] for t [tau], given the output of a nonlinear noisy sensor up to time t. The nonlinear filtering-smoothing problem is to estimate both xt and xt - [tau]. The optimal estimators are the conditional...

Stable law Gz admit a well-known series representation of the type where [Gamma]1, [Gamma]2, ... are the successive times of jumps of a standard Poisson process, and X1, X2, ..., denote i.i.d. random variables, independent of [Gamma]1, [Gamma]2, ... We investigate the rate of approximation of...

We consider the stochastic dynamics of infinitely many, interacting random closed strings, and show that the law of this process can be characterized as a Gibbs state for some Hamiltonian on the path level, which is represented in terms of the interaction. This is done by means of the stochastic...

An asymptotically finite bound is derived for the total variation distance between the distribution of N(t) and the Poisson distribution with mean EN(t) when N is a simple point process whose interpoint times are exponential with means determined by an ergodic, finite-state Markov chain and when...