Dynkin formula for Brownian motion (source code)

= Dynkin formula for Brownian motion
{c}
{wiki=Dynkin's_formula}

For a suitable twice differentiable function $u$ and an integrable stopping time $T$,
$$
\mathbb E_xu(B_T)=u(x)+\mathbb E_x\int_0^T\frac12\Delta u(B_t)\,dt.
$$