Geodesic
Inverse process with independent positive increments: finite-dimensional distributions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 286-297

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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. 
@article{ZNSL_2004_311_a16,
     author = {B. P. Harlamov},
     title = {Inverse process with independent positive increments: finite-dimensional distributions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {286--297},
     publisher = {mathdoc},
     volume = {311},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a16/}
}
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B. P. Harlamov. Inverse process with independent positive increments: finite-dimensional distributions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 7, Tome 311 (2004), pp. 286-297. http://geodesic.mathdoc.fr/item/ZNSL_2004_311_a16/