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Probabilistic and stochastic behavior are omnipresent in computer controlledsystems, in particular, so-called safety-critical hybrid systems, because offundamental properties of nature, uncertain environments, or simplifications toovercome complexity. Tightly intertwining discrete, continuous and stochasticdynamics complicates modelling, analysis and verification of stochastic hybridsystems (SHSs). In the literature, this issue has been extensivelyinvestigated, but unfortunately it still remains challenging as no promisinggeneral solutions are available yet. In this paper, we give our effort byproposing a general compositional approach for modelling and verification ofSHSs. First, we extend Hybrid CSP (HCSP), a very expressive and processalgebra-like formal modeling language for hybrid systems, by introducingprobability and stochasticity to model SHSs, which is called stochastic HCSP(SHCSP). To this end, ordinary differential equations (ODEs) are generalized bystochastic differential equations (SDEs) and non-deterministic choice isreplaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) tospecify and reason about SHCSP processes. We demonstrate our approach by anexample from real-world.

Extending Hybrid CSP with Probability and Stochasticity