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 ...

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 ...

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 ...

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 ...