高斯过程积分的加权幂变分
Weighted power variation of integrals with respect to a Gaussian process
摘要：
我们考虑一个随机过程$Y$，它由一个确定性函数$f$关于一个高斯过程$X$的二次平均积分定义，它不需要有平稳的增量。对一类高斯过程$X$，证明了$Y$在一个时间区间上的一系列分割上的增量的适当加权幂和几乎必然收敛.该结果的条件用$X$的协方差函数的$p$ -变差表示。特别地，当$X$是分数布朗运动、亚分数布朗运动和双分数布朗运动时，该结果成立。
英文摘要：
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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