Let (R) and (widetilde{R}) be two independent (mathrm{BES}^{3}) processes. The process (Y_{t}=R_{t}^{-1}-left(widetilde{R}_{t} ight)^{-1}) is a local martingale

Let \(R\) and \(\widetilde{R}\) be two independent \(\mathrm{BES}^{3}\) processes. The process \(Y_{t}=R_{t}^{-1}-\left(\widetilde{R}_{t}\right)^{-1}\) is a local martingale with null expectation. Prove that \(Y\) is a strict local martingale.

Let \(T_{n}\) be a localizing sequence of stopping times for \(1 / R\). If \(Y\) were a martingale, \(1 / \widetilde{R}_{t \wedge T_{n}}\) would also be a martingale. The expectation of \(1 / \widetilde{R}_{t \wedge T_{n}}\) can be computed and depends on \(t\).