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.
H. Wang et al., "Fundamental Structure of General Stochastic Dynamical Systems: High-Dimension Case," Journal of Mathematics, vol. 2022, article no. 2596074, Hindawi, Jan 2022.
The definitive version is available at https://doi.org/10.1155/2022/2596074
Mathematics and Statistics
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01 Jan 2022