Almost Sure Uniform Convergence of Stochastic Processes in the Dual of a Nuclear Space

Almost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...

Almost Sure Convergence to Zero in Stochastic Growth Models

This paper shows that in stochastic one-sector growth models, if the production function does not satisfy the Inada condition at zero, any feasible path converges to zero with probability one provided that the shocks are sufficiently volatile. This result seems significant since, as we argue, the Inada condition at zero is difficult to justify on economic grounds. Our convergence result is exte...

Almost sure convergence of stochastic gradient processes with matrix step sizes

We consider a stochastic gradient process, which is a special case of stochastic approximation process, where the positive real step size an is replaced by a random matrix An: Xn+1 = Xn Anrg(Xn) AnVn: We give two theorems of almost sure convergence in the case where the equation rg = 0 has a set of solutions. Key Words and Phrases: Stochastic approximation, stochastic gradient AMS 1991 Subject ...

Almost sure convergence of the Bartlett estimator

We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a. s. behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate nor...

On the uniform almost sure convergence of losses for the repetition of a statistical decision problem