Large-size populations consisting of a continuum identical and noncooperative agents with stochastic dynamics are useful in modeling various biological engineered systems. This article addresses the control problem designing optimal state-feedback controllers that guarantee closed-loop stability stationary density such nonlinear Langevin dynamics, under action their individual steady-state cont...

for the mean-square quantizing error where N is the. number of level&p(x) is the probability density of the input, and E’(x) is the slope of the compressor curve. The formula, an approximation based on the assumption that the number of levels is large and overI& distortion is negligible, is a useful tool for analytical studies of quantfzation. This paper gives a bedstlc argument generallhg Beme...

In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are straightforward if one assumes the sample size of each stage goes to infinity with the overall sample size. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experi...

In this paper we introduce a fully Bayesian approach to sample size determination in clinical trials. In contrast to the usual Bayesian decision theoretic methodology, which assumes a single decision maker, our approach recognises the existence of three decision makers, namely: the pharmaceutical company conducting the trial, which decides on its size; the regulator, whose approval is necessary...

In this study, a two-echelon supplier-manufacturer system with finite production rate and lead time is proposed. It is assumed that shortage is not permitted and the lot size of manufacturer (second echelon) is m-factors of the lot size of supplier (first echelon) and supplier can supply the manufacturer’s lot size in several shipments in each cyc...

We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f . The validity of these tests, in terms of exact finite sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests...