This paper studies the asymptotic properties of the kernel probability density estimate of stationary sequences which are observed through some non-linear instantaneous filter applied to long-range dependent Gaussian sequences. It is shown that the limiting distribution of the kernel estimator...

Suppose Xi, I = 1, 2, ... are i.i.d. positive random variables with d.f. F. We assume the tail d.f. to be regularly varying with 0 < [beta] < 1. The asymptotic behaviour of P(SN > x) as x -- [infinity] where SN = [Sigma]N1Xi and N,Xi(i = 1) independent with [Sigma][infinity]n=0P(N = n)xn analytic at x = 1 is studied under an additional...</[beta]>

We study the asymptotic behavior of solutions of differential equations dx[var epsilon](t)/dt = A(y(t/[var epsilon]))x[var epsilon](t), x[var epsilon](0) = x0, where A(y), for y in a space Y, is a family of operators forming the generators of semigroups of bounded linear operators in a Hilbert...

In this paper we show an approximation diffusion theorem for a stochastic integral equation on the plane driven by a two-parameter Wiener process. This result is obtained by means of the martingale problem approach for two-parameter processes.

We consider a process u[var epsilon](x,t), for x in a bounded interval, t [greater-or-equal, slanted] 0 and [var epsilon] a small parameter, given as the solution of a nonlinear heat equation perturbed by a space-time white noise multiplied by [var epsilon]. The nonlinear part is the derivative...

We study a one-dimensional nearest neighbor simple exclusion process for which the rates of jump are chosen randomly at time zero and fixed for the rest of the evolution. The ith particle's right and left jump rates are denoted pi and qi respectively; pi+ qi = 1. We fix c [epsilon] (1/2, 1) and...

Lam and Lehoczky (1991) have recently given a number of extensions of classical renewal theorems to superpositions of p independent renewal processes. In this article we want to advertise an approach that more explicitly uses a Markov renewal theoretic framework and thus leads to a simplified...

Let (L[theta])[theta][epsilon]N be a family of elliptic diffusion operators on a compact and connected smooth manifold M, whose terms of first order are indexed by a parameter [theta] living in N, the n-dimensional torus. For each fixed [theta], we associate to L[theta] its invariant probability...

Within the framework of transitive sufficient processes we investigate identifiability properties of unknown parameters. In particular we consider unbiased parameter estimators, which are shown to be closely connected to time reversal and to reverse martingales. One of the main results is that,...

Let M be a complete connected oriented Riemannian manifold of dimension n [greater-or-equal, slanted] 3; let X be a symmetrizable ergodic diffusion on M; let y be an oriented compact submanifold of M, of codimension 2; let Nt be the linking number between y and X [0, t]; then t-1 Nt converges in...