41 research outputs found
On high-frequency limits of -statistics in Besov spaces over compact manifolds
In this paper, quantitative bounds in high-frequency central limit theorems
are derived for Poisson based -statistics of arbitrary degree built by means
of wavelet coefficients over compact Riemannian manifolds. The wavelets
considered here are the so-called needlets, characterized by strong
concentration properties and by an exact reconstruction formula. Furthermore,
we consider Poisson point processes over the manifold such that the density
function associated to its control measure lives in a Besov space. The main
findings of this paper include new rates of convergence that depend strongly on
the degree of regularity of the control measure of the underlying Poisson point
process, providing a refined understanding of the connection between regularity
and speed of convergence in this framework.Comment: 19 page
Asymptotic theory for fractional regression models via Malliavin calculus
We study the asymptotic behavior as of the sequence
where and are two
independent fractional Brownian motions, is a kernel function and the
bandwidth parameter satisfies certain hypotheses in terms of
and . Its limiting distribution is a mixed normal law involving the
local time of the fractional Brownian motion . We use the techniques
of the Malliavin calculus with respect to the fractional Brownian motion
Density estimates for solutions to one dimensional Backward SDE's
In this paper, we derive sufficient conditions for each component of the
solution to a general backward stochastic differential equation to have a
density for which upper and lower Gaussian estimates can be obtained
On the law of the solution to a stochastic heat equation with fractional noise in time
We study the law of the solution to the stochastic heat equation with
additive Gaussian noise which behaves as the fractional Brownian motion in time
and is white in space. We prove a decomposition of the solution in terms of the
bifractional Brownian motion
Asymptotic Cram\'er type decomposition for Wiener and Wigner integrals
We investigate generalizations of the Cram\'er theorem. This theorem asserts
that a Gaussian random variable can be decomposed into the sum of independent
random variables if and only if they are Gaussian. We prove asymptotic
counterparts of such decomposition results for multiple Wiener integrals and
prove that similar results are true for the (asymptotic) decomposition of the
semicircular distribution into free multiple Wigner integrals