112 research outputs found
Asymptotic expansion for the quadratic form of the diffusion process
In [8], asymptotic expansion of the martingale with mixed normal limit was
provided. The expansion formula is expressed by the adjoint of a random symbol
with coefficients described by the Malliavin calculus, differently from the
standard invariance principle. As an application, an asymptotic expansion for a
quadratic form of a diffusion process was derived in the same paper. This
article gives some details of the derivation, after a short review of the
martingale expansion in mixed normal limit.Comment: arXiv admin note: text overlap with arXiv:1210.368
Second-order asymptotic expansion for a non-synchronous covariation estimator
In this paper, we consider the problem of estimating the covariation of two
diffusion processes when observations are subject to non-synchronicity.
Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, we derive second-order
asymptotic expansions for the distribution of the Hayashi-Yoshida estimator in
a fairly general setup including random sampling schemes and non-anticipative
random drifts. The key steps leading to our results are a second-order
decomposition of the estimator's distribution in the Gaussian set-up, a
stochastic decomposition of the estimator itself and an accurate evaluation of
the Malliavin covariance. To give a concrete example, we compute the constants
involved in the resulting expansions for the particular case of sampling scheme
generated by two independent Poisson processes
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