Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with ...

We supply some relations that establish intertwining from duality and give a probabilistic interpretation. This is carried out in the context of discrete Markov chains, fixing up the background of ...

Markov chain models and phase-type distributions have emerged as powerful tools in healthcare analytics, offering a robust framework for understanding and predicting patient trajectories throughout ...