Topics in Markov Additive Processes.

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

The 11th Workshop on Markov Processes and Related Topics

In this paper, we discuss an exponential integrator scheme, based on spatial discretization and time discretization, for a class of stochastic partial differential equations. We show that the scheme has a unique stationary distribution whenever the stepsize is sufficiently small, and that the weak limit of the stationary distribution of the scheme as the stepsize tends to zero is in fact the st...