First Crossing Times of Telegraph Processes with Jumps

Abstract

The paper presents exact formulae related to the distribution of the first passage time ?x of the jump-telegraph process. In particular, the Laplace transform of ?x is analysed, when a jump component is in the opposite direction to the crossing level x and gt; 0. The case of double exponential jumps is also studied in detail. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.