Distribution of some functionals for a Lévy process with matrix-exponential jumps of the same sign

Ie. V. Karnaukh

O. Honchar Dnipropetrovsk National University, 72, Gagarina Pr., Dnipropetrovsk 49010, Ukraine

Abstract: 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.

MSC: Primary 60G51; Secondary 60K10

Language: English

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