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?
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? 


try F. Herzberg at http://link.springer.com/chapter/10.1007/9783642331497_7 

