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...