A Path Transformation and its Applications to Fluctuation Theory

We first establish a combinatorial result on deterministic realchains. This is then applied to prove a path transformationfor chains with exchangeable increments. From this transformationwe derive an identity on order statistics due to Port, togetherwith some extensions. Then we give an interpretation of theseresults in continuous time. We extend some identities involvingquantiles and occupation times for processes with exchangeableincrements. In particular, this yields an extension of the uniformlaw for bridges obtained by Knight.