This paper considers the quantitative verification of discretetime stochastic hybrid systems (DTSHS) against linear time objectives. The central question is to determine the likelihood of all the trajectories in a DTSHS that are accepted by an automaton on finite or infinite words. This verification covers regular and ω-regular properties, and thus comprises the linear temporal logic LTL. This work shows that these quantitative verification problems can be reduced to computing reachability

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... bilities over the product of an automaton and the DTSHS under study. The computation of reachability probabilities can be performed in a backwardrecursive manner, and quantitatively approximated by procedures over discrete-time Markov chains. A case study shows the feasibility of the approach.