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Expansion of Perturbed Random Variables Based on Generalized Wiener Functionals

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  • Sakamoto, Yuji
  • Yoshida, Nakahiro
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    Abstract

    By means of the Malliavin calculus, we present an expansion formula for the distribution of a random variableFhaving a stochastic expansionF=F0+R, whereF0is an easily tractable random variable andRis the remainder term. From this result, we derive an expansion of the distribution of the scale mixturesZof a normal random variableZby a scale random variables. Applications to shrinkage estimators of the Stein type are mentioned

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 1 (October)
    Pages: 34-59

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:1:p:34-59

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    Keywords: Malliavin calculus asymptotic expansion scale mixture;

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    Cited by:
    1. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CIRJE F-Series CIRJE-F-654, CIRJE, Faculty of Economics, University of Tokyo.
    2. Masayuki Uchida & Nakahiro Yoshida, 2004. "Information Criteria for Small Diffusions via the Theory of Malliavin–Watanabe," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 35-67, March.
    3. Yuji Sakamoto & Nakahiro Yoshida, 2004. "Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(3), pages 545-597, September.
    4. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    5. Akihiko Takahashi & Kohta Takehara, 2009. "Asymptotic Expansion Approaches in Finance: Applications to Currency Options," CARF F-Series CARF-F-165, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    6. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    7. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.

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