Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations
Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations
复制标题
具有 K-Erlang 分布方向交替的有限速度各向同性随机运动
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Rodríguez
中科院分区：
文献类型：
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作者：
A. Pogorui;R. Rodríguez
我们研究了在有限速度下均匀分布的运动方向，其中根据K-Erlang函数的更新时代发生方向变化。乍一看，我们对以前的马尔可夫结果的推广似乎是一小步，然而，它必须被视为一个重要的非马尔可夫情况，我们已经找到了pdf的封闭形式表达式和这个半马尔可夫输运过程的条件特征函数。我们给出了2-Erlang情况下的三维例子的详细计算，这不仅从物理应用的角度来看很重要，而且对于理解更一般的模型也很重要。例如，原则上2-Erlang情况的例子可以扩展到K- erlang情况（K=3,4，…），但是一些数学表达式可能很麻烦。
We study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a K-Erlang pdf. At first sight, our generalizations of previous Markovian results appears to be a small step, however, it must be seen as an important non-Markovian case where we have found closed-form expressions for the pdf and the conditional characteristic function of this semi-Markov transport process. We present detailed calculations of a three-dimensional example for the 2-Erlang case, which is important not only from physical applications point of view but also to understand more general models. For instance, in principle the example of the 2-Erlang case can be extended to a K-Erlang case (K=3,4,…) but some of the mathematical expressions may be cumbersome.