Spline approximation of a random process with singularity
@article{Abramowicz2010SplineAO, title={Spline approximation of a random process with singularity}, author={Konrad Abramowicz and Oleg Seleznjev}, journal={Journal of Statistical Planning and Inference}, year={2010}, volume={141}, pages={1333-1342} }
7 Citations
Multivariate piecewise linear interpolation of a random field
- Mathematics
- 2011
We consider a multivariate piecewise linear interpolation of a continuous random field on a-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivar…
Piecewise-Multilinear Interpolation of a Random Field
- MathematicsAdvances in Applied Probability
- 2013
We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error.…
Uniform and non-uniform quantization of Gaussian processes
- Computer Science
- 2012
This work considers quantization of a signal (or random proscribed signal) into a discrete form (or discretization of amplitude) in all analog/digital devices.
Stratified Monte Carlo Quadrature for Continuous Random Fields
- Mathematics
- 2011
We consider the problem of numerical approximation of integrals of random fields over a unit hypercube. We use a stratified Monte Carlo quadrature and measure the approximation performance by the…
Approximation of a random process with variable smoothness
- Mathematics, Computer Science
- 2015
It is proved that the suggested approximation rate is optimal, and then it is shown how to find an optimal constant \(K\).
On Piterbarg Max-Discretisation Theorem for Standardised Maximum of Stationary Gaussian Processes
- Mathematics, Computer Science
- 2014
The joint limiting distribution of standardisedmaximum of a continuous, stationary Gaussian process and the standardised maximum of this process sampled at discrete time points are derived and it is proved that these two random sequences are asymptotically complete dependent if the grid of the discreteTime points is sufficiently dense, and asymPTotically independent if theGrid is sufficiently sparse.
References
SHOWING 1-10 OF 23 REFERENCES
Free-Knot Spline Approximation of Fractional Brownian Motion
- Mathematics
- 2008
For a fractional Brownian motion B H on [0,1], we consider approximations of B H by piecewise polynomial splines. Asymptotics of minimal average error rates are established and found to be of order k…
Good approximation by splines with variable knots. II
- Mathematics
- 1974
Consider approximation of a given function f, on [0,1] say, by elements of S π k , i.e., by polynomial splines of order k (or, degree < k) on some partition
$$({t_i})_0^{N + 1}of[0,1]\;0 = {t_0} <…
Spline Functions and Approximation Theory
- Mathematics
- 1973
DeVore, R. : Inverse Theorems For Approximation By Positive Linear Operators 371 Meir, A. & Sharma, A. : Lacunary Interpolation By Splines 377 Morris, P.D. & Cheney, E.W. : Stability Properties Of…
Sampling Designs for Estimation of a Random Process
- MathematicsProceedings. IEEE International Symposium on Information Theory
- 1993
A random process X(t), t[epsilon][0,1], is sampled at a finite number of appropriately designed points. On the basis of these observations, we estimate the values of the process at the unsampled…
Nonlinear Approximation of Random Functions
- MathematicsSIAM J. Appl. Math.
- 1997
It is shown that the nonlinear wavelet approximation is optimal in terms of mean square error and that this optimality is lost either by using the trigonometric system or by using any type of linear approximation method.
Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments
- Mathematics, Computer ScienceAdvances in Applied Probability
- 1996
We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance…
Good approximation by splines with variable knots +
- Mathematics
- 2011
Here, t1, . . . , tN are the knots or joints of s ∈ S k π, and their multiplicity, i.e., equality among two or more of these, indicates reduced smoothness at that knot location in the usual way. Best…