# First Crossing Times of Telegraph Processes with Jumps

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## Abstract

The paper presents exact formulae related to the distribution of the first passage time *τ*_{x} of the jump-telegraph process. In particular, the Laplace transform of *τ*_{x} is analysed, when a jump component is in the opposite direction to the crossing level *x* > 0. The case of double exponential jumps is also studied in detail.

## Keywords

Jump-telegraph process First passage time Laplace transformation Double exponential distribution## Mathematics Subject Classification (2010)

60J75 60J27 60K99## Preview

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## Notes

### Acknowledgments

I am very grateful to anonymous referees and the editor for the careful reading of the paper and for the helpful comments that have greatly improved the text.

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