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首页> 外文会议>World Multiconference on Systemics, Cybernetics and Informatics and 5th International Conference on Information Systems Analysis and Synthesis Vol.5: Computer Science and Engineering, Jul 31-Aug 4, 1999, Orlando, Florida >Mapped Markov chains for modeling non-Markovian processes
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Mapped Markov chains for modeling non-Markovian processes

机译：映射的马尔可夫链用于建模非马尔可夫过程

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摘要

We focus on stochastic processes which are deduced from time-discrete and finite-state Markov chains by mapping, in general, more than one Markov states to separated process elements which then are accessible for further application. We name these processes mapped Markov chains and demonstrate that they allow for unique treatment of its own. In general these processes are non-Markovian. For modeling required statistical characteristics we present a design procedure for the transition matrix of a steering Markov chain such that the finally mapped elements meet the proposed requirements. Analysis and synthesis are purely done by matrix calculus and general results are derived. In detail, we study the run-length distributions of the mapped elements and shortly discuss their linear complexity. We investigate a binary process specified by the run-length distribution of one element. We assume that this distribution is formed by the superposition of 2 simple geometric progressions thus inducing a basic non-Markovian property. We discuss the manifold of equivalent Markov chains for mapping and present its general solution. Numerical examples illustrate the theoretical results. Finally we consider the mutual information of the mapped processes with the steering Markov chains.
机译：我们关注于随机过程，该过程通常是通过将不止一个马尔可夫状态映射到分离的过程元素来从时离散和有限状态马尔可夫链推导而来的，这些元素随后可用于进一步的应用。我们将这些过程命名为映射的马尔可夫链，并证明它们允许对其自身进行独特处理。通常，这些过程是非马尔可夫过程。为了建模所需的统计特征，我们提出了转向马尔可夫链的过渡矩阵的设计程序，以使最终映射的元素满足建议的要求。分析和综合完全由矩阵演算完成，并得出一般结果。详细地，我们研究了映射元素的游程长度分布，并简要讨论了它们的线性复杂度。我们研究由一个元素的游程长度分布指定的二进制过程。我们假设此分布是由2个简单的几何级数的叠加形成的，从而得出基本的非马尔可夫性质。我们讨论了等效的马尔可夫链的流形用于映射，并提出了其一般解决方案。数值例子说明了理论结果。最后，我们考虑了带转向马尔可夫链的映射过程的互信息。

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