As written here, we have $f \in C_0$ in general. As discussed in comments, I wonder why/how $f \in C^2_0 $ for Brownian motion? I'd appreciate some explanation for the choice of space in the context of the definition of the infinitesimal generator.
2026-03-31 19:16:49.1774984609
Space of $f$ for infinitesimal generator of Brownian motion
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