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Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of Non-integer Orders

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Convexity and Concentration

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 161))

Abstract

This is mostly a review of results and proofs related to asymptotic expansions for characteristic functions of sums of independent random variables (known also as Edgeworth-type expansions). A number of known results is refined in terms of Lyapunov coefficients of non-integer orders.

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Acknowledgements

Sergey G. Bobkov would like to thank Irina Shevtsova for reading of the manuscript, valuable comments, and additional references.

Partially supported by the Alexander von Humboldt Foundation and NSF grant DMS-1612961.

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Authors and Affiliations

  1. University of Minnesota, Minneapolis, MN, 55455, USA

    Sergey G. Bobkov

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  1. Sergey G. Bobkov
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Correspondence to Sergey G. Bobkov .

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Editors and Affiliations

  1. Department of Mathematics, Rutgers University, Piscataway, New Jersey, USA

    Eric Carlen

  2. Department of Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    Mokshay Madiman

  3. Department of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

    Elisabeth M. Werner

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Bobkov, S.G. (2017). Asymptotic Expansions for Products of Characteristic Functions Under Moment Assumptions of Non-integer Orders. In: Carlen, E., Madiman, M., Werner, E. (eds) Convexity and Concentration. The IMA Volumes in Mathematics and its Applications, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7005-6_11

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