WALD EQUATIONS, FIRST PASSAGE TIMES AND MOMENTS OF LADDER VARIABLES IN MARKOV RANDOM-WALKS

Previous work in extending Wald's equations to Markov random walks inv olves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions . The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first pass age times of Markov random walks. Wiener-Hopf factorizations for Marko v random walks are also applied to analyse ladder variables and relate d first passage problems.