The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

In 1995, Pacheco and Prabhu introduced the class of so–called Markov–additive processes of arrivals in order to provide a general class of arrival processes for queueing theory. In this paper, the above class is generalized considerably, including time–inhomogeneous arrival rates, general phase spaces and the arrival space being a general vector space (instead of the finite–dimensional Euclidea...

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for...

We prove a functional central limit theorem for Markov additive arrival processes (MAAPs) where the modulating Markov process has the transition rate matrix scaled up by n (α > 0) and the mean and variance of the arrival process are scaled up by n. It is applied to an infinite-server queue and a fork-join network with a non-exchangeable synchronization constraint, where in both systems both the...

We consider the reliability of a single-unit system whose cumulative damage over time is a continuous wear process {X (t): t¿ 0} that depends on an external environment process {Z(t): t¿ 0}. We explicitly derive the failure time distribution and moments in terms of Laplace–Stieltjes transforms by analyzing the Markov additive process {(X (t); Z(t)): t¿ 0} and demonstrate its applicability on an...

– Studied in this paper is the transformation of an arbitrary symmetric Markov process X by multiplicative functionals which are the exponential of continuous additive functionals of X having zero quadratic variations. We characterize the transformed semigroups by their associated quadratic forms. This is done by first identifying the symmetric Markov process under Girsanov transform, which may...

We investigate the effects of noise reinforcement on a Bessel process dimension d?(0,2), and more specifically asymptotic behavior its additive functionals. This leads us to introduce local time inverse. identify latter as an increasing self-similar (time-homogeneous) Markov process, from this, several explicit results can be deduced.