I'll enjoy your kindness to ask this question, despite that it seems silly for you. Please show me a document or a url; emphasizing in a concise manner, the relationship between Brownian motion and Laplacian. With google, I found a lot of links; but I can not get the link to Markov chain, heat kernel and half Laplacian. friendly.
relationship between Brownian motion and $1 / 2 \Delta$
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probability-theory