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What is the definition of a conservative diffusion process? And diffusion operators?

I cannot find it on wiki or elsewhere...

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For a definition of a diffusion process you may consult Karatzas and Shreve 1991. Conservativness is a notion from the theory of Markov processes - References here are Ethier Kurtz or Kallenberg. – Julian Wergieluk Sep 22 '12 at 15:23

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