Free-Knot Spline Approximation of Stochastic Processes

2006/12/12 by Jakob Creutzig, Creutzig, J., Thomas Mueller-Gronbach +3
Economics, Econometrics and Finance · Engineering · Mathematics · #60G99 (Primary) 41A15 (Secondary) #65C30 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0612313

openalex publication_date 2006/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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