Let Rn = max0≤j≤n Sj − Sn be a random walk Sn reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times of Rn above horizontal or certain curved (power law) boundaries. Necessary and sufficient conditions are also given for the finiteness of the expected passage time of Rn above linear and square root boundaries. 2000 MSC Subject Classifications: prim...

Let Rt = sup0≤s≤t Xs − Xt be a Lévy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for Rt is finite, is given. We also discuss the almost sure finiteness of lim sup t→0 Rt/t , for each κ ≥ 0.

Let H be a Krull monoid with infinite cyclic class group G and let GP ⊂ G denote the set of classes containing prime divisors. We study under which conditions on GP some of the main finiteness properties of factorization theory—such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the exist...

A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent among finite sets of matrices is the subject of ongoing research. In this article we give a condition on a finite irreducible set of matrices which guarante...