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 ...

The Applied Probability Trust is a non-profit publishing foundation established in 1964 to promote study and research in the mathematical sciences. Its titles Journal of Applied Probability and ...

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 ...

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 ...

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 ...

This paper outlines a way to estimate transition matrices for use in credit risk modeling with a decades-old methodology that uses aggregate proportions data. This methodology is ideal for credit-risk ...