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We consider the problem of approximating the probability mass of the set oftimed paths under a continuous-time Markov chain (CTMC) that are accepted by adeterministic timed automaton (DTA). As opposed to several existing works onthis topic, we consider DTA with multiple clocks. Our key contribution is analgorithm to approximate these probabilities using finite difference methods.An error bound is provided which indicates the approximation error. Thestepping stones towards this result include rigorous proofs for themeasurability of the set of accepted paths and the integral-equation systemcharacterizing the acceptance probability, and a differential characterizationfor the acceptance probability.

Approximating Acceptance Probabilities of CTMC-Paths on Multi-Clock Deterministic Timed Automata