Kac's rescaling for jump-telegraph processes (Q451151)

The authors present some limit theorems for an asymmetric telegraph process with drift and jumps under different rescaling conditions. The jump-telegraph process is defined by the sum \(X(t):= T(t)+ J(t)\), \(t\geq 0\).NEWLINENEWLINE After an Introduction, in Section 2 Cauchy problems for transition probabilities of jump-telegraph processes are derived. The authors propose a rather new approach based on the integral equations instead of the usually used infinitesimal presentation.NEWLINENEWLINE In the next section the explicit formulae for the Fourier transform of the distribution are derived. The explicit formulae for characteristic function of jump-telegraph process obtained in this section allow the investigation of the limit behaviour of the telegraph process with jumps.NEWLINENEWLINE Thus, in the last section, the main results are given.NEWLINENEWLINE To the reviewer the study was a good and instructive read.