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Questions tagged [moment-problem]

The moment problem arises as the result of trying to invert the mapping that takes a measure $μ$ to the sequences of moments, and to resolve the problem of determinacy of such measure.

The moment problem arises as the result of trying to invert the mapping that takes a measure $μ$ to the sequences of moments, and to resolve the problem of determinacy of such measure. Please do not use this tag just because moments are involved.

161 questions
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Image of the moment operator

Suppose we have a sequence $(a_k)_k$ in $\mathbb{C}$. I am wondering under which conditions it is true that there is a function $f \in L^1 \left[ 0, 1 \right]$ such that $a_k$ is the k-th moment of $f$. I'm aware of Hausdorff's solution to the…
Bruno Krams
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Where shall we use fifth order or higher order moment?

I have seen to use moment up to fourth, but in general, the definition of moment tells for larger than four. I am wondering where we should use higher moment than four and what is the intuition towards data analysis as well as in complex networks.…
P Pradhan
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Is the following sequence a moment seqence?

Is the sequence $$\Bigl( \frac{1}{n+1} \Bigr)^\alpha,\quad n \geq 0$$ a moment sequence for any $\alpha \in (0,1]$ for some random variable on [0,1]? We have tried checking whether the corresponding matrix is positive definite, this did not show…
malin
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Moment in parallelogram

If F is a force in the same plane as parallelogram ABCD and the moment of F about A equals -18 moment unit and the moment about B equals the moment about D equals 32, what is the moment of F about C? The answer is 82 but I want to know how
Ahmed Hassan
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Uniqueness of a moment problem over $\int^{\infty}_{0} \frac{\sigma^p}{(1+\sigma)^{2S}} m(\sigma) \: \mathrm d \sigma$ with a finite range in $p$

A question over on the physics site asked about the moment problem $$ \int^{\infty}_{0} \frac{\sigma^p}{(1+\sigma)^{2S}} m(\sigma) \: \mathrm d \sigma = \frac{p!(2S-p)!}{(2S+1)!}, $$ where $S=0,1,2,\ldots$ and $p=0,1,2,\ldots,2S$, which turns out to…
E.P.
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