= Endpoint convergence of a bounded angle diffusion
{title2=$d\Theta=\cos\Theta\,dZ,\quad \Theta_\infty\in\{-\pi/2,\pi/2\}$}
A diffusion remaining in $(-\pi/2,\pi/2)$ with the displayed equation is a bounded <martingale> and has a terminal limit. Its expected total <quadratic variation> is finite by its bounded second moments. An interior limit would leave its squared diffusion coefficient bounded away from zero and force infinite <quadratic variation>. Thus it converges to an endpoint, and the preserved mean determines the two endpoint probabilities.
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