Heuristically, a discrete-time stochastic process has the Markov property if the past and
future are independent given the present. In this introductory chapter, we give the formal …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

We consider non‐conservative positive semigroups and obtain necessary and sufficient
conditions for uniform exponential contraction in weighted total variation norm. This ensures …

This paper establishes Hoeffding's lemma and inequality for bounded functions of general-
state-space and not necessarily reversible Markov chains. The sharpness of these results is …

Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs
samplers Page 1 Bernoulli 24(2), 2018, 842–872 DOI: 10.3150/15-BEJ785 Uniform ergodicity of …

Given a target probability density known up to a normalizing constant, the Metropolis–
Hastings algorithm simulates realizations from a Markov chain which are eventual …

The bouncy particle sampler is a Markov chain Monte Carlo method based on a
nonreversible piecewise deterministic Markov process. In this scheme, a particle explores …

This review paper, written for the second edition of the Handbook of Markov Chain Monte
Carlo, provides an introduction to the study of convergence analysis for Markov chain Monte …

We define the spectral gap of a Markov chain on a finite state space as the second-smallest
singular value of the generator of the chain, generalizing the usual definition of spectral gap …

One of the inherent challenges in deploying transformers on time series is that\emph {reality
only happens once}; namely, one typically only has access to a single trajectory of the data …