English

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.

Keywords

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

R2 v1 2026-06-23T13:31:57.648Z