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For a standard Brownian motion, the generator of the diffusion is $$ L = \frac12 \frac{d^2}{dx^2}. $$

Is there a nonstandard definition of this generator?

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up vote 1 down vote accepted

try F. Herzberg at http://link.springer.com/chapter/10.1007/978-3-642-33149-7_7

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