High-order Markov chain models extend the conventional framework by incorporating dependencies that span several previous states rather than solely the immediate past. This extension allows for a ...

We consider a singularly perturbed (finite state) Markov chain and provide a complete characterization of the fundamental matrix. In particular, we obtain a formula for the regular part simpler than a ...

Consider a stochastic process X on a finite state space X = {1,..., d}. It is conditionally Markov, given a real-valued “input process” ζ. This is assumed to be small, which is modeled through the ...

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 ...

I've heard of Markov Chains, but I didn't understand them until I visited this site that explains them with simple ...

What if you could predict the future, not with a crystal ball, but with math? In this guide, Veritasium explains how a 120-year-old concept called Markov chains has become a silent force shaping ...

In this episode probability mathematics and chess collide. In this episode probability mathematics and chess collide. What is the average number of steps it would take before a randomly moving knight ...

A Markov chain is a mathematical concept of a sequence of events, in which each future event depends only on the state of the previous events. Like most mathematical concepts, it has wide-ranging ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I closely examine an innovative way of ...