Abstract
Consider two independent Goldstein-Kac telegraph processes X1(t) and X2(t) on the real line R. The processes Xk(t), k = 1, 2, describe stochastic motions at finite constant velocities c1 > 0 and c2 > 0 that start at the initial time instant t = 0 from the origin of R and are controlled by two independent homogeneous Poisson processes of rates $λ1 > 0 and $λ2 > 0, respectively. We obtain a closed-form expression for the probability distribution function of the Euclidean distance ρ(t) = |X1(t) - X2(t)|, t > 0, between these processes at an arbitrary time instant t > 0. Some numerical results are also presented.
Citation
Alexander D. Kolesnik. "Probability distribution function for the Euclidean distance between two telegraph processes." Adv. in Appl. Probab. 46 (4) 1172 - 1193, December 2014. https://doi.org/10.1239/aap/1418396248
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