We characterize the convergence in distribution to a standard normal law for
a sequence of multiple stochastic integrals of a fixed order with variance
converging to 1. Some applications are given, in particular to study the
limiting behavior of quadratic functionals of Gaussian processes.Comment: Published at http://dx.doi.org/10.1214/009117904000000621 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
International audienceWe prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H > 0:5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by Hölder continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, under a suitable nondegeneracy conditio
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