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：本文利用一种源自分支粒子系统重标度占据时间过程波动极限的协方差函数，引入了一族加权长程相依高斯过程。特别地，我们考察了两个子族，证明了该过程不是半鞅，且过程呈现长程相依性并具有对数阶的长程记忆性。最后，我们通过实例说明该过程族对现实世界数据建模具有实用价值。