You can calculate a derivative of densities for stochastic processes in some generalised sense which I do not at present understand, and do the normal calculus thing you do with a derivative. Stochastic differential equations arise, presumably ones in some sense involving this generalised derivative, can then solve some kind of problems for you. Or something.

Clearly this is a placeholder for a topic I do not have time for right now. 🏗

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Zhang, Han. 2004. “The Malliavin Calculus.”