Asymptotic distributional theorems are presented for the maximal sojourn duration on a semi-Markov chain and for the first passage time until a lengthy duration. Our analysis characterizes the limiting behavior of the longest "generalized success outcome" on a semi-Markov chain. The models...

Let X = (X1, X2,..., Xn) be a random vector in Rn (Euclidean n-space) with density f(x). X or f(x) is said to be multivariate reverse rule of order 2 (MRR2) if f(x [curly logical or] y) f(x [curly logical and] y) = f(x) f(y) where the lattice operations x [curly logical and] y and x [curly...

A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) = f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2...

A dynamic inventory model is formulated in which the demand distributions may change from period to period. The optimal policy at each stage is characterized by a single critical number which also could vary in successive periods. The dependence of the critical numbers as a function of...