In this chapter we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very genera...

Unambiguous automata, i.e., nondeterministic automata with the restriction of having at most one accepting run over a word, have the potential to be used instead of deterministic automata in settings where nondeterministic automata can not be applied in general. In this paper, we provide a polynomially time-bounded algorithm for probabilistic model checking of discrete-time Markov chains agains...

The analysis of hybrid systems exhibiting probabilistic behaviour is notoriously difficult. To enable mechanised analysis of such systems, we extend the reasoning power of arithmetic satisfiability-modulo-theory solving (SMT) by a comprehensive treatment of randomized (a.k.a. stochastic) quantification over discrete variables within the mixed Boolean-arithmetic constraint system. This provides ...

Statistical model-checking is a recent technique used for both verification and performance analysis of hybrid systems. It does not suffer from decidability issues or state-space explosion compared to traditional model-checking. Furthermore, it is applicable to more powerful formalisms such as stochastic hybrid automata. Its principle is simple so how simple is it really to make it work in prac...

We consider optimization problems where the objective function is defined over some continuous and some discrete variables, and only noise corrupted values of the objective function are observable. Such optimization problems occur naturally in PAC learning with noisy samples. We propose a stochastic learning algorithm based on the model of a hybrid team of learning automata involved in a stocha...

Statistical model-checking is a recent technique used for both verification and performance analysis of hybrid systems. It does not suffer from decidability issues or state-space explosion compared to traditional model-checking. Furthermore, it is applicable to more powerful formalisms such as stochastic hybrid automata. Its principle is simple so how simple is it really to make it work in prac...

We present a new performance evaluation tool based on the analysis of large Markov chains and Stochastic Automata Networks. Using some graph theoretical arguments, we show how to systematically perform state reduction. The graph properties can be checked easily because we take advantage of the tensorial construction of the Markov chain from the Stochastic Automata Network.