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PERIODIC BOXCAR DECONVOLUTION AND DIOPHANTINE APPROXIMATION
BOXCAR DECONVOLUTION DIOPHANTINE APPROXIMATION
2015/8/20
We consider the nonparametric estimation of a periodic function that is
observed in additive Gaussian white noise after convolution with a “boxcar,”
the indicator function of an interval. This is an...
Trajectory averaging for stochastic approximation MCMC algorithms
Trajectory averaging MCMC algorithms
2010/11/18
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area...
Inhomogeneous theory of dual Diophantine approximation on manifolds
Metric Diophantine approximation extremal manifolds
2010/12/14
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is e...
Polynomial estimates, exponential curves and Diophantine approximation
Polynomial estimates exponential curves Diophantine approximation
2010/12/10
Let ∈ (0, 1) \ Q and K = {(ez, e z) : |z| ≤ 1} ⊂ C2. If P is a polynomial of degree n in C2, normalized by kPkK = 1, we obtain sharp estimates for kPk2 in terms of n, where 2 is the closed u...
On Simultaneous Approximation by a Linear Combination of a New Sequence of Linear Positive Operators
Simultaneous approximation Linear positive operators Linear combination Voronovskaja-type asymptotic formula Modulus of continuity
2010/2/26
In [1] we introduced a new sequence of linear positive operators Mn to approximate unbounded continuous functions of exponential growth on [0,\infty). As this sequence is saturated with O(n-1), to acc...