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The explicit probability distribution of the sum of two telegraph processes

The explicit probability distribution of the sum of two telegraph processes

We consider two independent Goldsteinā€“Kac telegraph processes X 1 (t) and X 2 (t) on the real line ā„, both developing with constant speed c > 0, that, at the initial time instant t = 0, simultaneously start from the origin 0 āˆˆ ā„ and whose evolutions are controlled by ā€¦