Is there a SDE for a (one-dimensional) reflected (at 0) drifted Brownian motion like $d X_t = \mu dt + \sigma d W_t$ for the normal Brownian motion?
2026-04-01 13:28:27.1775050107
Stochastic Differential Equation for a reflected Brownian motion
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As discussed in this blog post, reflected Brownian motion satisfies the SDE $$ dX_t=\textrm{sign}(B_t)\ dB_t, $$ where $X_t=|B_t|$ is the reflected Brownian motion, and $$ \textrm{sign}(x)=\begin{cases}1,&x>0\\0,&x=0\\-1,&x<0.\end{cases} $$