  We consider the problem of approximating the probability mass of the set of
timed paths under a continuous-time Markov chain (CTMC) that are accepted by a
deterministic timed automaton (DTA). As opposed to several existing works on
this topic, we consider DTA with multiple clocks. Our key contribution is an
algorithm to approximate these probabilities using finite difference methods.
An error bound is provided which indicates the approximation error. The
stepping stones towards this result include rigorous proofs for the
measurability of the set of accepted paths and the integral-equation system
characterizing the acceptance probability, and a differential characterization
for the acceptance probability.
