## Bernoulli

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

### Weighted power variation of integrals with respect to a Gaussian process

Rimas Norvaiša

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 21 April 2015

https://projecteuclid.org/euclid.bj/1429624978

Digital Object Identifier
doi:10.3150/14-BEJ606

Mathematical Reviews number (MathSciNet)
MR3338664

Zentralblatt MATH identifier
1326.60081

#### Citation

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. https://projecteuclid.org/euclid.bj/1429624978

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