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Malliavin calculus and asymptotic expansion for martingales
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  • Published: November 1997

Malliavin calculus and asymptotic expansion for martingales

  • Nakahiro Yoshida1 

Probability Theory and Related Fields volume 109, pages 301–342 (1997)Cite this article

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Summary.

We present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a continuous martingale. The emphasis is put on the use of the Malliavin calculus; the uniform nondegeneracy of the Malliavin covariance under certain truncation plays an essential role as the Cramér condition did in the case of independent observations. Applications to statistics are presented.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153, Japan, , , , , , JP

    Nakahiro Yoshida

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  1. Nakahiro Yoshida
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Received: 5 September 1995 / In revised form: 20 October 1996

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Yoshida, N. Malliavin calculus and asymptotic expansion for martingales. Probab Theory Relat Fields 109, 301–342 (1997). https://doi.org/10.1007/s004400050134

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  • Issue Date: November 1997

  • DOI: https://doi.org/10.1007/s004400050134

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  • Mathematics Subject Classification (1991): 60F05
  • 60G44
  • 62E20
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