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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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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DOI: https://doi.org/10.1007/s004400050134
- Mathematics Subject Classification (1991): 60F05
- 60G44
- 62E20