How to Construct Diffusion Processes on Metric Spaces

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We present a general method to construct m-symmetric diffusion processes (Xt, Px) on any given locally compact metric space (X, d) equipped with a Radon measure m. These processes are associated with local regular Dirichlet forms which are obtained as Γ-limits of approximating non-local Dirichlet forms. This general method works without any restrictions on (X, d, m).

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