Discover how Markov chains predict real systems, from Ulam and von Neumann’s Monte Carlo to PageRank, so you can grasp ...

A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...

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 ...

The probability distribution of the number of defaults plays an important role in pricing problems of multiple-name credit derivatives. When the group size gets large, it becomes increasingly ...