Excursion theory is applied to get identities for continuous time ladder variables. The identities are used to classify coharmonic and coinvariant functions for one dimensional Levy processes.
Martin L. Silverstein. "Classification of Coharmonic and Coinvariant Functions for a Levy Process." Ann. Probab. 8 (3) 539 - 575, June, 1980. https://doi.org/10.1214/aop/1176994726