Malliavin calculus and asymptotic expansion for martingales

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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 Cramer condition did in the case of independent observations. Applications to statistics are presented.

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