Passage-time moments for continuous non-negative stochastic processes and applications

The authors give criteria for the finiteness or infiniteness of the passage-time moments for continuous non-negative stochastic processes in terms of sub/supermartingale inequalities for powers of these processes. They apply these results to one-dimensional diffusions and also reflected Brownian motion in a wedge. The discrete-time analogue of this problem was studied previously by Lamperti and more recently by Aspandiiarov, Iasnogorodski and Menshikov. The present results are continuous analogues of theirs, but the proofs are direct and do not rely on approximation by discrete-time processes.