Three examples of Brownian flows on $\RR$

Yves Le Jan, Olivier Raimond

We show that the only flow solving the stochastic differential equation (SDE) on $\RR$ $$d{X}_t=1_{\{X_t>0\}}{W}_{+}(dt)+1_{\{X_t<0\}}d{W}_{-}(dt),$$ where $W^{+}$ and $W^{-}$ are two indepe…