Weak infinitesimal generators of a class of jump-perturbed Markov processes

Comparison of Markov processes via infinitesimal generators

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral versio...

Weak Conditioning for Jump Processes

We develop the theory of weak conditioning initiated in [2, 5] in a general framework for semimartingales with jumps. An example is given based on Lévy processes, for which the link to pure jump Schrödinger processes is exhibited. AMS 2000 Subject Classification : Primary: 60G07, 60G44; secondary: 60G51.

Markov Chains and Jump Processes

Data-Based Inference of Generators for Markov Jump Processes Using Convex Optimization

A variational approach to the estimation of generators for Markov jump processes from discretely sampled data is discussed and generalized. In this approach, one first calculates the spectrum of the discrete maximum likelihood estimator for the transition matrix consistent with the discrete data. Then the generator that best matches the spectrum is determined by solving a convex quadratic minim...

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...