In this article we use a covariance function that arises from limit of fluctuations of the rescaled occupation time process of a branching particle system, to introduce a family of weighted long-range dependence Gaussian processes. In particular, we consider two subfamilies for which we show that the process is not a semimartingale, that the processes exhibit long-range dependence and have long-range memory of logarithmic order. Finally, we illustrate that this family of processes is useful for modeling real world data.

翻译：本文利用一种协方差函数引入了一类加权长程依赖高斯过程，该函数源自分支粒子系统重标度占据时间过程涨落的极限。特别地，我们考察了两个子族，证明了该过程不是半鞅，且展现出对数阶的长程依赖性与长程记忆特性。最后，我们通过实例说明此类过程适用于现实世界数据的建模。