  We study the Parallel Replica Dynamics in a general setting. We introduce a
trajectory fragment framework that can be used to design and prove consistency
of Parallel Replica algorithms for generic Markov processes. We use our
framework to formulate a novel condition that guarantees an asynchronous
algorithm is consistent. Exploiting this condition and our trajectory fragment
framework, we present new synchronous and asynchronous Parallel Replica
algorithms for piecewise deterministic Markov processes.
