Cool! Other people interested in combinatorial stochastic processes. Long paper. Appears they use clever bijections to relate their objects of interest to Dyck paths and go from there, haven't even browsed closely tho.
J. Pitman. Lecture Notes in Mathematics Springer-Verlag, Berlin, (2006)Lectures from the 32nd Summer School on Probability Theory
held in Saint-Flour, July 7--24, 2002,
With a foreword by Jean Picard.