Geodesic
Distribution of some functionals for a L\'{e}vy process with matrix-exponential jumps of the same sign
Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 26-36

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This paper provides a framework for investigations in fluctuation theory for Lévy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we establish generalizations of some results known for compound Poisson processes with exponential jumps in one direction and generally distributed jumps in the other direction.
Keywords: Lévy processes; matrix-exponential jumps; extrema; overshoot; sojourn time; ladder process. 
@article{THSP_2014_19_1_a2,
     author = {Ie. V. Karnaukh},
     title = {Distribution of some functionals for a {L\'{e}vy} process with matrix-exponential jumps of the same sign},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {26--36},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a2/}
}
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Ie. V. Karnaukh. Distribution of some functionals for a L\'{e}vy process with matrix-exponential jumps of the same sign. Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 26-36. http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a2/