Model Checking Multivariate State Rewards

We consider continuous stochastic logics with state rewards that are interpreted over continuous time Markov chains. We show how results from multivariate phase type distributions can be used to obtain higher-order moments for multivariate state rewards (including covariance). We also generalise the treatment of eventuality to unbounded path formulae. For all extensions we show how to obtain closed form definitions that are straightforward to implement and we illustrate our development on a small example.