77 research outputs found
A Fourier transform method for nonparametric estimation of multivariate volatility
We provide a nonparametric method for the computation of instantaneous
multivariate volatility for continuous semi-martingales, which is based on
Fourier analysis. The co-volatility is reconstructed as a stochastic function
of time by establishing a connection between the Fourier transform of the
prices process and the Fourier transform of the co-volatility process. A
nonparametric estimator is derived given a discrete unevenly spaced and
asynchronously sampled observations of the asset price processes. The
asymptotic properties of the random estimator are studied: namely, consistency
in probability uniformly in time and convergence in law to a mixture of
Gaussian distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Unitarizing probability measures for representations of Virasoro algebra
AbstractDetermination of a formula of integration by part insuring the unitarity
Frame Bundle of Riemannian Path Space and Ricci Tensor in Adapted Differential Geometry
AbstractThe vanishing of the renormalized Ricci tensor of the path space above a Ricci flat Riemannian manifold is discussed
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