The problem of finding stopping rules which maximize (EXt) (EYt) is considered, for independent pairs (Xi, Yi) of nonnegative r.v.s. with known joint distribution. The solution is compared to that of maximizing E(Xt Yt). When (Xi, Yi) are uniform, a detailed analysis is given for the...

Optimum group maintenance policies for a set of N machines subjected to stochastic failures under continuous and periodic inspections are considered. Under very general conditions it is shown that a control limit policy minimizes the expected cost per unit time over an infinite horizon, when...

A dynamic programming problem is called invariant if its transition mechanism depends only on the action taken and does not depend on the current state of the systm. Replacement and maintenance problems are two typical types of problems which arise in applications and are often invariant. The...

The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t)≤exp(−B(t)) forB(t)=t22(σ2+ct)for  t≥0,andB(t)=tc(logt−loglogt−σ2c)for  te whenever there exists a zero biased coupling of Y bounded by c,...

The Robbins-Monro procedure is investigated for various choices of step sizes, including those of the form c / nlog n, c 0. Rates of convergence using this and other choices are compared to rates obtained using cn[beta], for . Of all choices considered, it is seen that a procedure of Fabian's...

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated...

A concentration of measure result is proved for the number of isolated vertices Y in the Erdos-Rényi random graph model on n edges with edge probability p. When [mu] and [sigma]2 denote the mean and variance of Y respectively, P((Y-[mu])/[sigma]=t) admits a bound of the form e-kt2 for some...

The moments of certain stochastic integrals with respect to Brownian motion are well known. In this paper the mean and variance of some integrals involving Brownian bridges are found.

Suppose you observe a finite sequence of random variables from some known joint distribution F, you can stop the process at any time and your profit is the last observed value. If an optimal stopping rule is used, denote the expected profit by VF. What kind of ordering on multivariate...