Journal of Applied Probability, Vol. 41, Stochastic Methods and Their Applications (2004), pp. 347-360 (14 pages) This paper investigates the probabilistic behaviour of the eigenvalue of the empirical ...

We describe a computational procedure for evaluating the quasi-stationary distributions of a continuous-time Markov chain. Our method, which is an 'iterative version' of Arnoldi's algorithm, is ...

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 ...

Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of ...

Amid all the hype about AI it sometimes seems as though the world has lost sight of the fact that software such as ChatGPT contains no intelligence. Instead it’s an extremely sophisticated system for ...

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 ...

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 ...

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 ...