Concept

Stieltjes moment problem

In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2, ...) to be of the form for some measure μ. If such a function μ exists, one asks whether it is unique. The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞). Let and Then { mn : n = 1, 2, 3, ... } is a moment sequence of some measure on with infinite support if and only if for all n, both { mn : n = 1, 2, 3, ...

Official source

https://en.wikipedia.org/wiki/Stieltjes_moment_problem

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Damir Filipovic

Damir Filipovic holds the Swissquote Chair in Quantitative Finance and is Swiss Finance Institute Professor at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Prior to this, he was head of the Vienna Institute of Finance and professor at the University of Vienna. He previously held the chair of financial and insurance mathematics at the University of Munich, and he was on the faculty of Princeton University. He received his Ph.D. in mathematics from ETH Zurich in 2000. Damir Filipovic worked as a scientific consultant for the Swiss Federal Office of Private Insurance from 2003 to 2004. There he co-developed the Swiss Solvency Test, which defines the regulatory capital requirement for all Swiss based insurance companies and groups. He is on the editorial board of several academic journals. His research interests include the term structure of interest rates, credit and volatility risk, quantitative methods in risk management, and stochastic processes. His papers have been published in a variety of academic journals including the Journal of Financial Economics, Mathematical Finance, Finance and Stochastics, and the Annals of Applied Probability. He is the author of a textbook titled Term-Structure Models.

Related concepts (2)

Hamburger moment problem

In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there exist a positive Borel measure μ (for instance, the measure determined by the cumulative distribution function of a random variable) on the real line such that In other words, an affirmative answer to the problem means that (m0, m1, m2, ...) is the sequence of moments of some positive Borel measure μ.

Moment problem

In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequence of moments More generally, one may consider for an arbitrary sequence of functions Mn. In the classical setting, μ is a measure on the real line, and M is the sequence { xn : n = 0, 1, 2, ... }. In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique.

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Official source

https://en.wikipedia.org/wiki/Stieltjes_moment_problem

About this result

Related lectures (5)

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Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.

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Related publications (2)

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arXiv2025

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We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is th

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Related people (1)

Damir Filipovic

Related concepts (2)

Hamburger moment problem

Moment problem