We give upper and lower bounds for the probability for a local extrema of a totally skewed [alpha]-stable stochastic process. Often these bounds are sharp and coincide. The Gaussian case [alpha]=2 is not excluded, and there our results slightly improve existing general bounds. Applications focus...

Let V(X1,...,Xn) denote the total edge length of the Voronoi tessellation on random variables X1,...,Xn. If X1,X2,... are independent and have a common continuous density f(x) on the unit square which is bounded away from 0 and [infinity] then it is shown thatwhere c.c. denotes complete convergence.

Non-Gaussian limiting distributions of the rescaling solutions of the heat equation for non-Gaussian initial data with long-range dependence are discribed in terms of their multiple stochastic integral representations.

Based on recent results on the exploitation of "drift criteria" for general state-space Markov processes, we derive rates of convergence for (moments of ) processes associated with a renewal process with common inter-renewal time distribution F. Some of the results are classical and some are...

An infinite system of stochastic differential equations for the locations and weights of a collection of particles is considered. The particles interact through their weighted empirical measure, V, and V is shown to be the unique solution of a nonlinear stochastic partial differential equation...

We present some results of convergence for a minimum contrast estimator in a problem of change-points estimation. Here, we consider that the changes affect the marginal distribution of a sequence of random variables. We only consider parametric models, but the results are obtained under very...

The purpose of this paper is to propose a unifying weak dependence condition. Mixing sequences, functions of associated or Gaussian sequences, Bernoulli shifts as well as models with a Markovian representation are examples of the models considered. We establish Marcinkiewicz-Zygmund, Rosenthal...

Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604-622), Ji and Chizeck (1990, Automat....

Consider the nonparametric estimation of a multivariate regression function and its derivatives for a regression model with long-range dependent errors. We adopt local linear fitting approach and establish the joint asymptotic distributions for the estimators of the regression function and its...

Let {X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} be a stochastic process whose range is a random Cantor-like set depending on an [alpha]-sequence (0[alpha]1) and [mu] is the occupation measure of X(t). In this paper we examine the multifractal structure of [mu] and obtain...