= Projection unboundedness of a uniformly elliptic diffusion
For an SDE with bounded drift and diffusion coefficients and $\sum_k\langle\xi,\sigma_k(x)\rangle^2\ge\lambda|\xi|^2$, each fixed nonzero scalar projection of a solution is unbounded in absolute value almost surely. Rescale a slab to $(-1,1)$; its projected drift is controlled by its uniformly positive bracket density. The <exit with drift controlled by quadratic variation> then forces exit from every slab in a countable exhaustion.
// Target: probability-and-statistics.bigb
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