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February, 1995 Predicting Integrals of Stochastic Processes
Michael L. Stein
Ann. Appl. Probab. 5(1): 158-170 (February, 1995). DOI: 10.1214/aoap/1177004834


Consider predicting an integral of a stochastic process based on $n$ observations of the stochastic process. Among all linear predictors, an optimal quadrature rule picks the $n$ observation locations and the weights assigned to them to minimize the mean squared error of the prediction. While optimal quadrature rules are usually unattainable, it is possible to find rules that have good asymptotic properties as $n \rightarrow \infty$. Previous work has considered processes whose local behavior is like $m$-fold integrated Brownian motion for $m$ a nonnegative integer. This paper obtains some asymptotic properties for quadrature rules based on median sampling for processes whose local behavior is not like $m$-fold integrated Brownian motion for any $m$.


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Michael L. Stein. "Predicting Integrals of Stochastic Processes." Ann. Appl. Probab. 5 (1) 158 - 170, February, 1995.


Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0820.62081
MathSciNet: MR1325047
Digital Object Identifier: 10.1214/aoap/1177004834

Primary: 62M20
Secondary: 41A55

Keywords: design of time series experiments , fractional Brownian motion , median sampling , Optimal quadrature , Riemann zeta function

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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