Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case

Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao and M. M. Bhatti

Journal of Mathematics, 2022, vol. 2022, 1-24

Abstract: No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2596074

DOI: 10.1155/2022/2596074

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