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Normal moments and Hermite polynomials

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  • Willink, R.

Abstract

Hermite polynomials are used to derive expressions for the moments about the origin of univariate and multivariate normal distributions. A recurrence relation derived for multivariate Hermite polynomials leads to a recurrence relation for the multivariate normal moments.

Suggested Citation

  • Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:3:p:271-275
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    References listed on IDEAS

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    1. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
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    Cited by:

    1. Lorenzo Garlappi & Georgios Skoulakis, 2009. "Numerical Solutions to Dynamic Portfolio Problems: The Case for Value Function Iteration using Taylor Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 33(2), pages 193-207, March.
    2. Withers, Christopher S. & Nadarajah, Saralees, 2010. "Some conditional expectation identities for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2250-2253, October.
    3. Yang, Nian & Chen, Nan & Wan, Xiangwei, 2019. "A new delta expansion for multivariate diffusions via the Itô-Taylor expansion," Journal of Econometrics, Elsevier, vol. 209(2), pages 256-288.
    4. Wei, Zhengyuan & Zhang, Xinsheng, 2008. "A matrix version of Chernoff inequality," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1823-1825, September.
    5. Wan, Xiangwei & Yang, Nian, 2021. "Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    6. Chao Huang & Martin Styner & Hongtu Zhu, 2015. "Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 946-961, September.
    7. Song, Iickho & Lee, Seungwon, 2015. "Explicit formulae for product moments of multivariate Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 27-34.
    8. Sun, Ping, 2007. "Moment representation of Bernoulli polynomial, Euler polynomial and Gegenbauer polynomials," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 748-751, April.

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