Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions

Almost sure convergence of randomly truncated stochastic algorithms under verifiable conditions

Abstract. In this paper, we are interested in the almost sure convergence of randomly truncated stochastic algorithms. In their pioneer work, Chen and Zhu (1986) required that the family of the noise terms is summable to ensure the convergence. In our paper, we present a new convergence theorem which extends the already known results by making vanish this condition on the noise terms — a condit...

Asymptotic normality of randomly truncated stochastic algorithms

On almost sure and mean square convergence of P-type ILC under randomly varying iteration lengths

This note proposes convergence analysis of iterative learning control (ILC) for discrete-time linear systems with randomly varying iteration lengths. No prior information is required on the probability distribution of randomly varying iteration lengths. The conventional P-type update law is adopted with Arimoto-like gain and/or causal gain. The convergence both in almost sure and mean square 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 Kernel Bivariate Distribution Function Estimator under Negative Association

Let {Xn ,n=>1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) for fixed $K /in N$ based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth...