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Jan 20, 2022 at 11:03 comment added Dima Pasechnik all the moments are seldom known in such a settting. Sometimes one can say something about a moment generating function though, and derive something from the latter.
Jan 20, 2022 at 5:39 comment added Weather Report OK, but I do not assume that the moments are given. Rather, I'm interested to look at the situation when the measure is known explicitly, it's critical points are hard to find, but the moments can still be computed.
Jan 19, 2022 at 21:08 comment added Dima Pasechnik You are, essentially, trying to find the best Dirac measure appoximating your measure.
Jan 19, 2022 at 18:53 comment added Weather Report I think the difference with my question is that I assume that the measure $\mu$ is known, but it's difficult to find its critical points directly.
Jan 19, 2022 at 17:46 history answered Dima Pasechnik CC BY-SA 4.0