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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - Ie. V. Karnaukh
TI  - Distribution of some functionals for a L\'{e}vy process with matrix-exponential jumps of the same sign
JO  - Teoriâ slučajnyh processov
PY  - 2014
SP  - 26
EP  - 36
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a2/
LA  - en
ID  - THSP_2014_19_1_a2
ER  - 
%0 Journal Article
%A Ie. V. Karnaukh
%T Distribution of some functionals for a L\'{e}vy process with matrix-exponential jumps of the same sign
%J Teoriâ slučajnyh processov
%D 2014
%P 26-36
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a2/
%G en
%F THSP_2014_19_1_a2
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/

[1] A. E. Kyprianou, Introductory Lectures on Fluctuations of Levy Processes with Applications, Springer, New York, 2006 | MR | Zbl

[2] N. Bratiychuk, D. Husak, Boundary-Values Problems for Processes with Independent Increments, Naukova Dumka, Kyiv, 1990 (in Russian)

[3] A.L̇. Lewis, E. Mordecki, “Wiener-Hopf factorization for Levy processes having negative jumps with rational transforms”, J. of Appl. Prob., 45:1 (2008), 118–134 | DOI | MR | Zbl

[4] D. Landriault, J. F. Renaud, X. Zhou, “Occupation times of spectrally negative Lévy processes with applications”, Stochastic processes and their applications, 212:11 (2011), 2629–2641 | DOI | MR

[5] D. Husak, Processes with Independent Increments in Risk Theory, Institute of Mathematics of the NAS of Ukraine, Kyiv, 2011 (in Ukrainian)

[6] A. Kuznetsov, A. E. Kyprianou, J. C. Pardo, “Meromorphic Levy processes and their fluctuation identities”, Ann. of Appl. Prob., 22:3 (2012), 1101–1135 | DOI | MR | Zbl

[7] S. Asmussen, H. Albrecher, Ruin Probabilities, World Scientific, Singapore, 2010 | MR | Zbl

[8] M. W. Fackrell, Characterization of Matrix-exponential Distributions, PhD Thesis, The University of Adelaide, 2003

[9] M. Bladt, B. F. Nielsen, “Multivariate matrix–exponential distributions”, Stochastic Models, 26:1 (2010), 1–26 | DOI | MR | Zbl

[10] J. Bertoin, Lévy Processes, Cambridge Univ. Press, Cambridge, 1996 | MR