I have a question that is more of a reference request.
Let $(X_t,\mathcal{F}_t)_{t \geq 0}$ be a Cauchy summetric process. Assume that it is $n$ dimensional. Then a little research helped me find the distribution function for any $t$. It is given by:
$$f_t(x):=\frac{\Gamma(\frac{1+d}{2})\cdot t}{\pi^{(1+d)/2}[1+(x-\mu)'(x-\mu)]^{\frac{1+d}{2}}} \quad x,\mu \in \mathbb{R}^d$$
My question is: how can we express $dX_t$? I am pretty sure it is a martingale (please comment on this) and hence $dX_t=f(B_t,x)dB_t$ for some function $f$. What is this function $f$ then? Thanks id advance!