随机加速粒子在正半轴上的占据时间：前五个矩的结果
Occupation time of a randomly accelerated particle on the positive half axis: Results for the first five moments
摘要：
在随机加速过程中，一维运动的点粒子被均值为零的高斯白噪声加速。虽然已经详细分析了运动的几个基本统计特性，但对占据时间的统计仍然没有很好的理解。我们考虑粒子在无界$x$轴上随机加速一段时间$t$，在正$x$轴上的占据或停留时间$T_+$.最近Ouandji Boutcheng等人在\cite{OB}中推导出了$T_+$的前两个矩。利用基函数的另一种方法，已被证明是有用的随机加速运动的其他研究中，本文获得的前五个时刻的结果。
英文摘要：
In the random acceleration process a point particle moving in one dimension is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the statistics of occupation times is still not well understood. We consider the occupation or residence time $T_+$ on the positive $x$ axis of a particle which is randomly accelerated on the unbounded $x$ axis for a time $t$. The first two moments of $T_+$ were recently derived by Ouandji Boutcheng et al. \cite{OB}. With an alternate approach utilizing basis functions which have proved useful in other studies of randomly accelerated motion, results for the first five moments are obtained in this paper.
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