On the asymmetric telegraph processes

We study the one-dimensional random motionX = X(t), t 0, which takes two different velocities with two different alternating intensities. The closed-form formulae for the density functions of X and for the moments of any order, as well as the distributions of the first passage times, are obtained. The limit behaviour of the moments is analysed under nonstandard Kac's scaling. © Applied Probability Trust 2014