The Case of General Symmetric Markov Processes

Abstract

We now explain briefly how some of the above results can be extended to symmetric Markov processes on continuous spaces. The construction of the loop measure as well as a lot of computations can be performed quite generally, using Markov processes or Dirichlet space theory (Cf. for example [10]). $\mathbb{P}_\text{t} ^{x,y}$can be properly defined. The semigroup should have a density with respect to the duality measure given by a locally integrable kernel p_t(x, y). This is very often the case in examples of interest, especially in finite dimensional spaces.