Properties of the telegrapher's random process with or without a trap

Probabilistic analysis of the telegrapher′s process with drift by means of relativistic transformations

“…The Lorentz transformation discussed in Section 3 permits us to derive the distribution p(x, t)dx Pr{X(t) e dx} from that of p--p(x',t'). By exploiting well known results in literature (see [3,8]) we can express p(x', t') as follows: is the zero-order Bessel function with imaginary argument. In view of a result in [8] we can also write the expression for the flow function w-w(x',t') in the following We now present what we consider the most important result in this paper.…”

“…The classical case (c 1 c 2 c;I 12 1) has been studied in many papers and important probabilistic distributions and representations have been obtained independently by various authors and by different methods (for example, Orsingher [8], Foong [2], Foong and Kanno [3], Kabanov [4]). …”

Estimation for the discretely observed telegraph process

“…Many authors analyzed probabilistic properties of the process over the years (see e.g. Orsingher [16] and [17]; Pinsky [18]; Fong and Kanno [7]; Stadje and Zacks [21]). Di Crescenzo and Pellerey [4] proposed the geometric telegraph process as a model to describe the dynamics of the price of risky assets, i.e.…”

Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations

“…V (0) (with values ±c). Properties of this process (including first-passage time distributions) are studied in Foong and Kanno [8] and a telegraph process with random velocities has been recently considered by Stadje and Zacks [19]. For n = 1, β = 1 and ν = 1 2 the special equation…”