Jump Markov chains and rejection-free Metropolis algorithms

Markov Chains and Jump Processes

On Metropolis-Hastings algorithms with delayed rejection

On the convergence of the Metropolis-Hastings Markov chains

In this paper we consider Metropolis-Hastings Markov chains with absolutely continuous with respect to Lebesgue measure target and proposal distributions. We show that under some very general conditions the sequence of the powers of the conjugate transition operator has a strong limit in a properly defined Hilbert space described for example in Stroock [17]. Then we propose conditions under whi...

Markov Chains and Polynomial Time Algorithms

This paper outlines the use of rapidly mixing Markov Chains in randomized polynomial time algorithms to solve approximately certain counting problems. They fall into two classes : combinatorial problems like counting the number of perfect matchings in certain graphs and geometric ones like computing the volumes of convex sets.

Markov Chains Approximation of Jump-Diffusion Quantum Trajectories

“Quantum trajectories” are solutions of stochastic differential equations also called Belavkin or Stochastic Schrödinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually considered, one is driven by a one-dimensional Brownian motion and the other is driven by a counting process. In this article, we present a way to obtain more adva...