Irreversible samplers from jump and continuous Markov processes

Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers

Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions.We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-co...

From Markov jump processes to spatial queues

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Safety Verification of Continuous-Space Pure Jump Markov Processes

We study the probabilistic safety verification problem for pure jumpMarkov processes, a class of models that generalizes continuous-time Markov chains over continuous (uncountable) state spaces. Solutions of these processes are piecewise constant, right-continuous functions from time to states. Their jump (or reset) times are realizations of a Poisson process, characterized by a jump rate funct...

Markov Chains and Jump Processes

Sufficiency of Markov Policies for Continuous-Time Markov Decision Processes and Solutions of Forward Kolmogorov Equation for Jump Markov Processes

In continuous-time Markov decision processes (CTMDPs) with Borel state and action spaces, unbounded transition rates, for an arbitrary policy, we construct a relaxed Markov policy such that the marginal distribution on the stateaction pairs at any time instant is the same for both the policies. This result implies the existence of a relaxed Markov policy that performs equally to an arbitrary po...