We extend the definition of level-crossing ordering of stochastic processes, proposed by Irle and Gani (2001), to the case in which the times to exceed levels are compared using an arbitrary ...

In this paper we study polynomial and geometric (exponential) ergodicity for M/G/1-type Markov chains and Markov processes. First, practical criteria for M/G/1-type Markov chains are obtained by ...

Markov processes form a fundamental class of stochastic models in which the evolution of a system is delineated by the memoryless property. In such processes, the future state depends solely on the ...

This is a graduate-level course focused on techniques and models in modern discrete probability. Topics include: the first and second moment methods, martingales, concentration inequalities, branching ...

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 ...

This course is compulsory on the BSc in Actuarial Science and BSc in Actuarial Science (with a Placement Year). This course is available on the BSc in Data Science, BSc in Financial Mathematics and ...

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 ...