On Markov-Additive Jump Processes

The Optimal Filtering of Markov Jump Processes in Additive White Noise

Additive subordination and its applications in finance

This paper studies additive subordination, which we show is a useful technique for constructing time-inhomogeneous Markov processes with analytical tractability. This technique is a natural generalization of Bochner’s subordination that has proven to be extremely useful in financial modelling. Probabilistically, Bochner’s subordination corresponds to a stochastic time change with respect to an ...

Spatial Queues

In the present thesis, a theoretical framework for the analysis of spatial queues is developed. Spatial queues are a generalization of the classical concept of queues as they provide the possibility of assigning properties to the users. These properties may influence the queueing process, but may also be of interest for themselves. As a field of application, mobile communication networks are mo...

Non-markovian Limits of Additive Functionals of Markov Processes

Abstract. In this paper we consider an additive functional of an observable V (x) of a Markov jump process. We assume that the law of the expected jump time t(x) under the invariant probability measure π of the skeleton chain belongs to the domain of attraction of a subordinator. Then, the scaled limit of the functional is a Mittag-Leffler proces, provided that Ψ(x) := V (x)t(x) is square integ...

Moments of Transition-Additive Random Variables Defined on Finite, Regenerative Random Processes

Random processes consisting of a sequence of jumps from one to another of a finite set of states are considered. Such processes are regenerative if the progress after the nth jump depends only upon the state entered at the jump. Examples include discrete and continuous Markov processes. A method is given to restrict attention to a subset of sample paths according to criteria based on the transi...