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Markov process representation of semigroups whose generators include negative rates. (English) Zbl 07252787
Summary: 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.
MSC:
60J27 Continuous-time Markov processes on discrete state spaces
60J35 Transition functions, generators and resolvents
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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. · Zbl 1173.82020
[2] Sabine Jansen and Noemi Kurt, On the notion(s) of duality for markov processes, Probab. Surveys 11 (2014), 59-120. · Zbl 1292.60077
[3] Anja Sturm, Jan M.
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