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?



Nonstandard definition for the generator of a standard Ito diffusion
try F. Herzberg at <http://link.springer.com/chapter/10.1007/978-3-642-33149-7_7>


