• Bernoulli
  • Volume 21, Number 2 (2015), 1260-1288.

Weighted power variation of integrals with respect to a Gaussian process

Rimas Norvaiša

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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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Bernoulli, Volume 21, Number 2 (2015), 1260-1288.

First available in Project Euclid: 21 April 2015

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covariance double Riemann–Stieltjes integral Gaussian process locally stationary increments Orey index power variation $p$-variation quadratic mean integral


Norvaiša, Rimas. Weighted power variation of integrals with respect to a Gaussian process. Bernoulli 21 (2015), no. 2, 1260--1288. doi:10.3150/14-BEJ606.

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