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Free-Knot Spline Approximation of Stochastic Processes

Probability 2007-05-23 v1

Abstract

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 ss-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average LpL_p-distance to the splines spaces, as the (expected) number kk of free knots tends to infinity.

Keywords

Cite

@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}
}

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23 pages