A generalized telegraph process with velocity driven by random trials. (English) Zbl 1291.60182
This interesting paper deals with a one-dimensional telegraph-type random motion where the velocities are randomly chosen at the occurences of the governing process. The additional randomness is supposed to be either Bernoulli or Pólya. In the first case the new velocity is independent of the previous evolution while in the second case a memory of the past motion is introduced. The intertimes between events changing the velocity of motion are independent, absolutely continuous, positive random variables. Within this generalized context the authors are able to obtain the probability laws of motions and in some specific cases also in a closed form. Fine results are provided in all cases considered but expecially for the Bernoulli case.
Reviewer: Enzo Orsingher (Roma)
Keywords:
telegraph process; random intertime; random velocity; Bernoulli scheme; Pólya urn model; logistic stationary densityReferences:
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