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Exact Asymptotics for the Distribution of the Time of Attaining the Maximum for a Trajectory of a Compound Poisson Process with Linear Drift
Siberian Advances in Mathematics Pub Date : 2020-03-17 , DOI: 10.3103/s1055134420010034 V. E. Mosyagin
Siberian Advances in Mathematics Pub Date : 2020-03-17 , DOI: 10.3103/s1055134420010034 V. E. Mosyagin
We consider the random process at − v+(pt) + v−(−qt), t ∈ (−∞, −), where v− and v+ are independent standard Poisson processes if t ≥ 0 and v−(t) = v+(t) = 0 if t < 0. Under certain conditions on the parameters a, p, and q, we study the distribution function G = G(x) of the time of attaining the maximum for a trajectory of this process. In the present article, we find an exact asymptotics for the tails of G. We also find a connection between this problem and the statistical problem of estimation of an unknown discontinuity point of a density function.
中文翻译:
线性漂移复合泊松过程轨迹达到最大值的时间的精确渐近分布
我们认为,随机过程在- v +(PT)+ v - ( - QT),吨∈(-∞, - ),其中v -和v +是独立的标准泊松过程如果吨≥0和v - (吨) = v +(t)= 0如果t <0。在某些条件下关于参数a,p和q,我们研究分布函数G = G(x)达到此过程轨迹的最大值的时间。在本文中,我们找到了G尾部的精确渐近线。我们还发现了该问题与估计密度函数未知不连续点的统计问题之间的联系。
更新日期:2020-03-17
中文翻译:
线性漂移复合泊松过程轨迹达到最大值的时间的精确渐近分布
我们认为,随机过程在- v +(PT)+ v - ( - QT),吨∈(-∞, - ),其中v -和v +是独立的标准泊松过程如果吨≥0和v - (吨) = v +(t)= 0如果t <0。在某些条件下关于参数a,p和q,我们研究分布函数G = G(x)达到此过程轨迹的最大值的时间。在本文中,我们找到了G尾部的精确渐近线。我们还发现了该问题与估计密度函数未知不连续点的统计问题之间的联系。