  Stochastic HYPE is a novel process algebra that models stochastic,
instantaneous and continuous behaviour. It develops the flow-based approach of
the hybrid process algebra HYPE by replacing non-urgent events with events with
exponentially-distributed durations and also introduces random resets. The
random resets allow for general stochasticity, and in particular allow for the
use of event durations drawn from distributions other than the exponential
distribution. To account for stochasticity, the semantics of stochastic HYPE
target piecewise deterministic Markov processes (PDMPs), via intermediate
transition-driven stochastic hybrid automata (TDSHA) in contrast to the hybrid
automata used as semantic target for HYPE. Stochastic HYPE models have a
specific structure where the controller of a system is separate from the
continuous aspect of this system providing separation of concerns and
supporting reasoning. A novel equivalence is defined which captures when two
models have the same stochastic behaviour (as in stochastic bisimulation),
instantaneous behaviour (as in classical bisimulation) and continuous
behaviour. These techniques are illustrated via an assembly line example.
