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The Hausdorff moment problem under finite additivity

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Abstract
We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.
Keywords
coherent lower prevision, Hausdorff moment problem, lower distribution function, complete monotonicity

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Citation

Please use this url to cite or link to this publication:

Chicago
Miranda, Enrique, Gert De Cooman, and Erik Quaeghebeur. 2007. “The Hausdorff Moment Problem Under Finite Additivity.” Journal of Theoretical Probability 20 (3): 663–693.
APA
Miranda, E., De Cooman, G., & Quaeghebeur, E. (2007). The Hausdorff moment problem under finite additivity. Journal of Theoretical Probability, 20(3), 663–693.
Vancouver
1.
Miranda E, De Cooman G, Quaeghebeur E. The Hausdorff moment problem under finite additivity. Journal of Theoretical Probability. SPRINGER/PLENUM PUBLISHERS; 2007;20(3):663–93.
MLA
Miranda, Enrique, Gert De Cooman, and Erik Quaeghebeur. “The Hausdorff Moment Problem Under Finite Additivity.” Journal of Theoretical Probability 20.3 (2007): 663–693. Print.
@article{376551,
  abstract     = {We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.},
  author       = {Miranda, Enrique and De Cooman, Gert and Quaeghebeur, Erik},
  issn         = {0894-9840},
  journal      = {Journal of Theoretical Probability},
  keyword      = {coherent lower prevision,Hausdorff moment problem,lower distribution function,complete monotonicity},
  language     = {eng},
  number       = {3},
  pages        = {663--693},
  publisher    = {SPRINGER/PLENUM PUBLISHERS},
  title        = {The Hausdorff moment problem under finite additivity},
  url          = {http://dx.doi.org/10.1007/s10959-007-0055-4},
  volume       = {20},
  year         = {2007},
}

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