In this paper we consider the problem of estimating the parameters of a Markov model using so-called macro data. It will be shown that the stochastic process of the macro data is a Markov chain, which ...

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 ...

In this paper, we consider the asymptotic behavior of stationary probability vectors of Markov chains of GI/G/1 type. The generating function of the stationary probability vector is explicitly ...

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 ...

Quantum Markov chains (QMCs) represent a natural quantum extension of classical Markov processes, encapsulating memoryless dynamics within quantum systems. They offer a powerful framework to model non ...

Markov Models for disease progression are common in medical decision making (see references below). The parameters in a Markov model can be estimated by observing the time it takes patients in any ...