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Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds
Concentration Inequalities Confidence Bands Density Estimators
2011/3/21
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
A functional central limit theorem under uniform mixing on a locally compact Abelian group
A functional central limit theorem uniform mixing a locally compact Abelian group
2009/9/22
A central limit theorem and a corresponding functional
central h i t theorem are given under a uniform mixing condition for
uniformly inf~tesimal triangular arrays of random variables which
take va...
Martingale characterizations of stochastic processes on compact groups
Martingale characterizations of stochastic processes compact groups
2009/9/22
By a classical result of P. Lbvy, the Brownian motion
(Btjtb0 on R may be characterized as a continuous process on R such
that (B,),,, and (3;-t),,, are martingales. Generalizations of this
result ...
Snell's optimization problem for sequences of convex compact valued random sets
Snell's optimization problem sequences of convex valued random sets
2009/9/21
A random set analogue of the Snell problem is presented.
In the original Snell's problem one observes a sequence of random
variables (t,), say a gambler's capital at successive games. If the gambler...
On normalizers and centralizers of compact Lie groups. Applications to structural probability theory
Exponent commuting exponent operator-semistable law operator-stable law
2009/9/21
The concept of operator stability on finitedimensional
vector spaces V was generalized in the past into several directions. In
particular, operator-semistable and self-decomposable laws and self-
-...
SMALL DEVIATION OF SUBORDINATED PROCESSES OVER COMPACT SETS
Subordinator fractional Brownian motion covering numbers Gamma process
2009/9/18
Let A =
A(t)
t0 be a subordinator. Given a compact set
K [0;1) we prove two-sided estimates for the covering numbers of the
random set {A(t) : t 2 K} which depend on the Lapl...
On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups
isotropic Gaussian fields homogeneous spaces compact groups
2009/3/30
Let $T$ be a random field weakly invariant under the action of a compact group $G$. We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. As a ...
On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups
characterization homogeneous spaces compact groups
2009/3/23
Let $T$ be a random field weakly invariant under the action of a compact group $G$. We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. ...