A path transformation and its applications to fluctuation theory

We first establish a combinatorial result on deterministic real chains. Thi s is then applied to prove a path transformation for chains with exchangeab le increments. From this transformation we derive an identity on order stat istics due to Port, together with some extensions. Then we give an interpre tation of these results in continuous time. We extend some identities invol ving quantiles and occupation times for processes with exchangeable increme nts. In particular, this yields an extension of the uniform law for bridges obtained by Knight.