Søren Asmussen : Terminal distributions of skipfree Markov additive processes with absorbtion
نویسنده
چکیده
Let X be a Markov additive process with continuous paths and a finite background Markov process J so that X evolves as Brownian motion with drift r(i) and variance σ2(i) when J(t) = i. Assuming that J is eventually absorbed at some state a, the density f(x) of Z = X(ζ) is found where ζ is the absorbtion time. The form of f(x) is non-smooth at x = 0, but the distributions of Z+ and Z− are both of phase-type. The derivation involves concepts and results from fluctuation theory such as the Markov processes obtained by sampling J when X is at a relative maximum or minimum. The details are somewhat different for the fluid case where σ2(i) = 0 for all i and the Brownian case σ2(i) > 0.
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