Conditioning the tanh-drift process on first-passage times: Exact drifts, bridges, and process equivalences

Kacim François-Élie, Alain Mazzolo

In this article, we consider the Benes process with drift $\hat{I}¼(x)=\hat{I}\pm \tanh (\hat{I}\pm x+{\hat{I}}^2)$, with $\hat{I}\pm >0$, ${\hat{I}}^2\in \mathbb{R}$, that is, the diffusion defined by the stochastic differential…