Inverse process with independent positive increments: finite-dimensional distributions

An inverse process with independent positive increments is considered. For such a procees the first hitting time $\tau_x$ of the level $x$ as a function of $x\ge0$ is the proper process with independent positive increments. In terms of the first hitting times and their L'evy measures malti-demensional distribution densities and Laplace transformations are derived. Stationary distributions of increments of the process are being investigated.