I am considering a bounded, continuous function $f$ on $\mathbb{R}^d$.
For $X_t$ being a $d$-dimensional Uhlenbeck Ornstein process with $\theta=\sigma=1$, and for $x\in \mathbb{R}^d$, I want to show the following
$\lim_{t\rightarrow 0}\frac{E[f(X_t)]-f(x)}{t}=\frac{1}{2}\Delta f(x)-x\cdot\nabla f(x)$
I have assume that $f$ has bounded and continuous second order derivatives, but I can't get further than that...
Does anybody have some hints?