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Modeling of continuous time homogeneous Markov system with fixed size as elastic solid: the two-dimensional case

机译：固定大小为弹性固体的连续时间齐次马尔可夫系统的建模：二维情况

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摘要

Every attainable structure of a continuous time homogeneous Markov system (HMS) with n states and fixed size is considered as a point-particle of R~n. Thus, the motion of an attainable structure corresponds to the motion of the respective point-particle in R~n. Under the assumption that "the motion of every particle at every time point is due to its interaction with its surroundings", R~n becomes a continuum [Appl. Stochastic Models Data Anal. 13 (1998) 177]. The evolution of the set of the attainable structures corresponds to the motion of the continuum. For the particular case of a two-dimensional HMS (n = 2), it is examined to what extend the HMS could be considered as a linear elastic continuum (rod). Hence, it is concluded that the general concept of multidimensional anisotropic elasticity can further interpret the evolution of HMSs with n > 3.
机译：具有n个状态和固定大小的连续时间齐次马尔可夫系统（HMS）的每个可获得的结构都被视为R〜n的点粒子。因此，可达到的结构的运动对应于R〜n中各个点粒子的运动。在“每个粒子在每个时间点的运动是由于其与周围环境的相互作用”的假设下，R〜n成为一个连续体。随机模型数据肛门。 13（1998）177]。这组可达到的结构的演化对应于连续体的运动。对于二维HMS（n = 2）的特殊情况，要检查HMS在多大程度上可以视为线性弹性连续体（棒）。因此，可以得出结论，多维各向异性弹性的一般概念可以进一步解释n> 3的HMS的演化。

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