Multivariate Wide-sense Markov Processes and Prediction Theory

Wide-sense regeneration for Harris recurrent Markov processes: an open problem

Harris recurrence is a widely used tool in the analysis of queueing systems. For discrete-time Harris chains, such systems automatically exhibit wide-sense regenerative structure, so that renewal theory can be applied to questions related to convergence of the transition probabilities to the equilibrium distribution. By contrast, in continuous time, the question of whether all Harris recurrent ...

Multivariate prediction and matrix Szegö theory

Following the recent survey by the same author of Szegö’s theorem and orthogonal polynomials on the unit circle (OPUC) in the scalar case, we survey the corresponding multivariate prediction theory and matrix OPUC (MOPUC). AMS 2000 subject classifications: Primary 60G10; secondary 60G25.

Bootstrap prediction regions for multivariate autoregressive processes

Riassunto: L’obiettivo del presente lavoro è studiare il comportamento di una nuova procedura per la determinazione di regioni di previsione per processi autoregressivi multidimensionali. Le regioni di previsione, basate sulla tecnica bootstrap, non fanno affidamento su alcuna assunzione distributiva per i disturbi ed inoltre tengono conto della variabilità derivante dalla necessità di stimare ...

MA3H2 Markov Processes and Percolation theory

Cascade Markov Decision Processes: Theory and Applications

This paper considers the optimal control of time varying continuous time Markov chains whose transition rates are themselves Markov processes. In one set of problems the solution of an ordinary differential equation is shown to determine the optimal performance and feedback controls, while some other cases are shown to lead to singular optimal control problems which are more difficult to solve....