Joint Hitting-Time Densities for Finite State Markov Processes
نویسندگان
چکیده
For a finite state Markov process and a finite collection {Γk, k ∈ K} of subsets of its state space, let τk be the first time the process visits the set Γk. We derive explicit/recursive formulas for the joint density and tail probabilities of the stopping times {τk, k ∈ K}. The formulas are natural generalizations of those associated with the jump times of a simple Poisson process. We give a numerical example and indicate the relevance of our results to credit risk modeling.
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