Let (R) be a (mathrm{BES}^{3}) process starting from 1. Compute (mathbb{E}left(R_{t}^{-1} ight)). From the absolute continuity relationship

Let \(R\) be a \(\mathrm{BES}^{3}\) process starting from 1. Compute \(\mathbb{E}\left(R_{t}^{-1}\right)\).

From the absolute continuity relationship

\[\mathbb{E}\left(R_{t}^{-1}\right)=\mathbf{W}_{1}\left(T_{0}>t\right)=\mathbb{P}(|G|<1 / \sqrt{t})\]

where \(G\) is a standard Gaussian r.v..