Time at which the maximum of a random acceleration process is reached

Time at which the maximum of a random acceleration process is reached
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随机加速过程达到最大值的时间

DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Zoia
A. Zoia
中科院分区：
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文献类型：
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作者：
S. Majumdar;A. Rosso;A. Zoia

文献摘要

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我们研究的随机加速度模型，这也许是一个最简单的，但非平凡的，非马尔可夫随机过程，是许多应用的关键。对于这个非马尔可夫过程，我们提出了精确的分析结果的概率密度p（tm|在一个固定的时间间隔[0，T]内，该过程达到其最大值的时间tm。我们研究了两种不同的边界条件，它们分别对应于表示（i）布朗桥的积分和（ii）自由布朗运动的积分的过程。我们的分析结果也验证了数值模拟。
We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the probability density p(tm|T) of the time tm at which the process reaches its maximum, within a fixed time interval [0, T]. We study two different boundary conditions, which correspond to the process representing respectively (i) the integral of a Brownian bridge and (ii) the integral of a free Brownian motion. Our analytical results are also verified by numerical simulations.