Exit with drift controlled by quadratic variation

For a continuous local martingale $M$ with divergent bracket $K$ and a continuous drift $D$ satisfying $|D_t-D_s|\le C(K_t-K_s)$, the process $y+M+D$, $|y|<1$, exits $(-1,1)$ almost surely. In unit bracket time a Brownian increment of absolute size greater than $C+2$ forces exit within one unit, giving a geometric survival bound. The inverse bracket clock transfers this finite exit to ordinary time.

// Target: probability-and-statistics.bigb