Free-Knot Spline Approximation of Stochastic Processes

Details Free-Knot Spline Approximation of Stochastic Processes Free-Knot Spline Approximation of Stochastic Processes

2006-12-12

arxiv.org/abs/math/0612313v1

Mathematics

Probability

23 pages

Scientific paper

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

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