Is there a way to prove that the inverse Bessel process $|B_t|^{-1}$ is a local martingale without using Ito's formula, considering that the Green's function
$$g(x)=\int_0^\infty p(t,x)dt=(2\pi^{d/2})^{-1} \Gamma(d/2-1)|x|^{2-d}$$
(with $p(t,x)$ as transition density of the three dimensional Brownian motion) is harmonic?
($|\cdot|$ should be the Euclidean norm.)