Markov process representation of semigroups whose generators include negative rates

Florian Völlering

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arXiv · 2002.01805

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.

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Florian Völlering. 2020-02-05. Markov process representation of semigroups whose generators include negative rates. https://arxiv.org/abs/2002.01805

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