1ST-PASSAGE TIME, MAXIMUM DISPLACEMENT, AND KAC SOLUTION OF THE TELEGRAPHER EQUATION

The distributions of the first-passage time for the Poisson random walk on a straight line (also known as the telegrapher random process) subject to a given number of reversals in the walk are obtained explicitly for both the starting directions. These distributions are then used to obtain, again explicitly, the corresponding distributions of the maximum of the walk, proving the conjecture by Orsingher [Stochastic Process. Appl. 34, 49 (1990)] for the one started moving to the right. The latter distribution leads to a reinterpretation of Kac's solution of the telegrapher equation.