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Spline approximatio...
Abstract
Ämnesord
Stäng
- Let a continuous random process X defined on [0,1] be (m+β)-smooth, 0m, 0<β1, in quadratic mean for all t>0 and have an isolated singularity point at t=0. In addition, let X be locally like a m-fold integrated β-fractional Brownian motion for all nonsingular points. We consider approximation of X by piecewise Hermite interpolation splines with n free knots (i.e., a sampling design, a mesh). The approximation performance is measured by mean errors (e.g., integrated or maximal quadratic mean errors). We construct a sequence of sampling designs with asymptotic approximation rate n^(m+β) for the whole interval.
Nyckelord
- Approximation
- Random process
- Sampling design
- Hermite splines
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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