Electronic Communications in Probability

Markov process representation of semigroups whose generators include negative rates

Florian Völlering

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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

Electron. Commun. Probab., Volume 25 (2020), paper no. 67, 7 pp.

Received: 27 April 2020
Accepted: 9 September 2020
First available in Project Euclid: 22 September 2020

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Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Markov semigoups negative jump rates stochastic representation duality

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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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