Markov chains provide a fundamental framework for modelling stochastic processes, where the next state depends solely on the current state. Hidden Markov models (HMMs) extend this framework by ...

What Is Markov Chain Monte Carlo? Markov Chain Monte Carlo (MCMC) is a powerful technique used in statistics and various scientific fields to sample from complex probability distributions. It is ...

We consider discrete-time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which ...

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous ...