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May 2015 Weighted power variation of integrals with respect to a Gaussian process
Rimas Norvaiša
Bernoulli 21(2): 1260-1288 (May 2015). DOI: 10.3150/14-BEJ606


We consider a stochastic process $Y$ defined by an integral in quadratic mean of a deterministic function $f$ with respect to a Gaussian process $X$, which need not have stationary increments. For a class of Gaussian processes $X$, it is proved that sums of properly weighted powers of increments of $Y$ over a sequence of partitions of a time interval converge almost surely. The conditions of this result are expressed in terms of the $p$-variation of the covariance function of $X$. In particular, the result holds when $X$ is a fractional Brownian motion, a subfractional Brownian motion and a bifractional Brownian motion.


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Rimas Norvaiša. "Weighted power variation of integrals with respect to a Gaussian process." Bernoulli 21 (2) 1260 - 1288, May 2015.


Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1326.60081
MathSciNet: MR3338664
Digital Object Identifier: 10.3150/14-BEJ606

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability


Vol.21 • No. 2 • May 2015
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