Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs

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.