Free-Knot Spline Approximation of Stochastic Processes
概率论
2007-05-23 v1
摘要
We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the -fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average -distance to the splines spaces, as the (expected) number of free knots tends to infinity.
引用
@article{arxiv.math/0612313,
title = {Free-Knot Spline Approximation of Stochastic Processes},
author = {J. Creutzig and T. Mueller-Gronbach and K. Ritter},
journal= {arXiv preprint arXiv:math/0612313},
year = {2007}
}
备注
23 pages