Free-Knot Spline Approximation of Stochastic Processes

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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.
23 pages

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Probability, 65C30, 60G99 (Primary) 41A15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/99995

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0612313
 http://arxiv.org/abs/math/0612313

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arXiv