A one-sided symbol for It？-Lévy processes

A one-sided symbol of a one-sided bounded It\^o-L\'evy process is introduced and possible ways for its computation as well as its relation to the infinitesimal generator of the process are provided. Further, an integral criterion for invariant distributions of the underlying process is derived which relies on the one-sided symbol. Several applications in settings of one-sided bounded as well as unbounded processes illustrate the advantages of the new criterion in comparison to previous methods.