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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.
60J27 Continuous-time Markov processes on discrete state spaces
60J35 Transition functions, generators and resolvents
Full Text: DOI Euclid
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