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 pt(x, y). This is very often the case in examples of interest, especially in finite dimensional spaces.
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© 2011 Springer-Verlag Berlin Heidelberg
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Jan, Y.L. (2011). The Case of General Symmetric Markov Processes. In: Markov Paths, Loops and Fields. Lecture Notes in Mathematics(), vol 2026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21216-1_10
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DOI: https://doi.org/10.1007/978-3-642-21216-1_10
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Online ISBN: 978-3-642-21216-1
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