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October 27, 2017 14:15, Mathematical Colloquim, Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
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Moment determinacy of probability distributions
J. Stoyanovab a Newcastle University, United Kingdom
b Bulgarian Academy of Sciences, Sofia, Bulgaria
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Abstract:
We deal with distributions (or measures), one-dimensional or multi-dimensional, with finite all moments. It is well-known that any such a distribution is either uniquely determined by its moment (M-determinate) or it is non-unique (M-indeterminate). This is the classical moment problem originated in works by Chebyshev, Markov and Stieltjes. Well-known are general conditions which are "iff", but they cannot be checked. Thus our discussion will be on easier and checkable conditions for either uniqueness or non-uniqueness applied to probability distributions.
The emphasis will be on some recent developments such as:
- Krein's condition. Converse Krein's condition and Lin's condition.
- Stieltjes classes for M-indeterminate distributions. Index of dissimilarity.
- Hardy's condition. Multidimensional moment problem.
- Rate of growth of the moments for (in)determinacy.
There will be results, some of them very new, hints for their proof, examples and counterexamples, and also open questions.
Language: English
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