On two-dimensional extensions of Bougerol's identity in law

Yuu Hariya, Yohei Matsumura

Let $B=\{B_t{\}}_{t\ge 0}$ be a one-dimensional standard Brownian motion and denote by $A_t,t\ge 0$, the quadratic variation of $e^{B_t},t\ge 0$. The celebrated Bougerol'…