We construct loop soups for general Markov processes without transition densities and show that the associated permanental process is equal in distribution to the loop soup local time. This is used to establish isomorphism theorems connecting the local time of the original process with the associated permanental process. Further properties of the loop measure are studied.
"Markovian loop soups: permanental processes and isomorphism theorems." Electron. J. Probab. 19 1 - 30, 2014. https://doi.org/10.1214/EJP.v19-3255