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Approximating integrals of stochastic processes: extensions

Part of: Inference from stochastic processes Approximations and expansions

Published online by Cambridge University Press:  14 July 2016

Karim Benhenni
Karim Benhenni*
Affiliation:
Université Pierre Mendès France
*
∗Postal address: LABSAD, Bâtiment des Sciences Humaines et Mathématiques, Université Pierre Mendès France, BP 47 X, 38040 Grenoble, France. Email address: benhenni@labsad.upmf-grenoble.fr.
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Abstract

We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.

Keywords

Euler-MacLaurin formulaHölder regularity conditionsampling designRiemann zeta functionrate of convergence

MSC classification

Primary: 62M20: Prediction
Secondary: 41A25: Rate of convergence, degree of approximation 41A55: Approximate quadratures
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 843 - 855
Copyright
Copyright © Applied Probability Trust 1998 

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