Markov process representation of semigroups whose generators include negative rates
Probability
2020-09-11 v2
Abstract
Generators of Markov processes on a countable state space can be represented as finite or infinite matrices. One key property is that the off-diagonal entries corresponding to jump rates of the Markov process are non-negative. Here we present stochastic characterizations of the semigroup generated by a generator with possibly negative rates. This is done by considering a larger state space with one or more particles and antiparticles, with antiparticles being particles carrying a negative sign.
Cite
@article{arxiv.2002.01805,
title = {Markov process representation of semigroups whose generators include negative rates},
author = {Florian Völlering},
journal= {arXiv preprint arXiv:2002.01805},
year = {2020}
}
Comments
9 pages, compared to previous version includes some additional explanations and a further example regarding the growth of the semigroup; accepted in ECP