Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 25 (2020), paper no. 67, 7 pp.
Markov process representation of semigroups whose generators include negative rates
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.
Article information
Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 67, 7 pp.
Dates
Received: 27 April 2020
Accepted: 9 September 2020
First available in Project Euclid: 22 September 2020
Permanent link to this document
https://projecteuclid.org/euclid.ecp/1600740162
Digital Object Identifier
doi:10.1214/20-ECP349
Zentralblatt MATH identifier
07252787
Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]
Keywords
Markov semigoups negative jump rates stochastic representation duality
Rights
Creative Commons Attribution 4.0 International License.
Citation
Völlering, Florian. Markov process representation of semigroups whose generators include negative rates. Electron. Commun. Probab. 25 (2020), paper no. 67, 7 pp. doi:10.1214/20-ECP349. https://projecteuclid.org/euclid.ecp/1600740162