You know I'm guessing, but logic seems to say this:

The shadow is cast by the opaque hair parts and not by the transparent hair parts.

The definition of what is opaque and what is transparent here is the transparency map of the hair.

Transmaps are subject to the same aliasing problems as any other map.

Grainy results are usually the result of failure to react to aliasing problems.

Therefore I'm guessing the map needs anti-aliasing.

Either:

Use render settings that will address aliasing

or

Use texture filtering on the transmap.

or

Go into an image editing program and make a smaller, less-detailed version of the transmap. Use that instead.

Anthanasius gave good input on the render settings: pixel samples 4 to 6 will reduce aliasing problems. Also note that sampling of the map is controlled by the min shading rate, so one would also want the min shading rate down to .2 before looking elsewhere for the problem.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)