Markov Additive Processes and Repeats in Sequences

Linear Additive Markov Processes

We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parameterization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its stead...

On Markov-Additive Jump Processes

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...

Fluctuations of spectrally negative Markov additive processes

This paper presents some fluctuation identities for a special, but none the less quite general, class of Markov Additive Processes (MAP). Before entering our discussion on the subject we shall simply begin by defining the class of processes we intend to work with and its properties. Following Asmussen and Kella (2000) we consider a process X(t), where X(t) = X(t) +X(t), and the independent proc...

The KTH Visit in Semi-Markov Processes

First passage of time-reversible spectrally negative Markov additive processes

We study the first passage process of a spectrally-negative Markov additive process (MAP). The focus is on the background Markov chain at the times of the first passage. This process is a Markov chain itself with a transition rate matrix Λ. Assuming time-reversibility we show that all the eigenvalues of Λ are real with algebraic and geometric multiplicities being the same, which allows us to id...