Electronic Communications in Probability

Markov process representation of semigroups whose generators include negative rates

Florian Völlering

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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


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References

  • [1] Cristian Giardina, Jorge Kurchan, Frank Redig, and Kiamars Vafayi, Duality and hidden symmetries in interacting particle systems, Journal of Statistical Physics 135 (2009), no. 1, 25–55.
  • [2] Sabine Jansen and Noemi Kurt, On the notion(s) of duality for markov processes, Probab. Surveys 11 (2014), 59–120.
  • [3] Anja Sturm, Jan M. Swart, and Florian Völlering, The algebraic approach to duality: An introduction, Genealogies of Interacting Particle Systems (Matthias Birkner, Rongfeng Sun, and Jan M. Swart, eds.), World Scientific Publishing, 2020, pp. 81–150.