Thank you for your answer. It should be high enough (refraction 10), because if I replace the mia material with a simple maya shader, and make it transparent, then it works.
The water material has a solid option (the surfaces should be have a proper exit/entry) in advanced refraction, and I use a simple plain for water, but if I change to the thin walled the caustics doesn't work again. So I leave this solid.
I found something. I replaced the pool itself with a simple extruded cube, and it works, the water transparent and has caustics. But I can't understand what is wrong with the sill. It has a displacement map, and mentalraySubdivApprox, and its material is a blinn with displacement in its blinnSG.
I really worked hard on displacement map, so I would like to use it.