  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.
