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Probability Distribution Function for the Euclidean Distance Between Two Telegraph Processes

  • Alexander D. Kolesnik (a1)

Abstract

Consider two independent Goldstein-Kac telegraph processes X 1(t) and X 2(t) on the real line ℝ. The processes X k (t), k = 1, 2, describe stochastic motions at finite constant velocities c 1 > 0 and c 2 > 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) = |X 1(t) - X 2(t)|, t > 0, between these processes at an arbitrary time instant t > 0. Some numerical results are also presented.

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Copyright

Corresponding author

Postal address: Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academy Street 5, Kishinev 2028, Moldova. Email address: kolesnik@math.md

References

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Probability Distribution Function for the Euclidean Distance Between Two Telegraph Processes

  • Alexander D. Kolesnik (a1)

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