多元受控自回归滑动平均系统的Rényi熵
Rényi entropy for multivariate controlled autoregressive moving average systems
AI总结：
本文针对多元受控自回归滑动平均系统，推导了输出过程Rényi熵的显式公式，并通过仿真和两个实际应用验证了其行为。
摘要：
Rényi熵作为香农熵的推广，是信息论中的一个重要度量。该信息度量常用于随机过程动态行为的不确定性量化。本文详细研究了多元受控自回归滑动平均（MCARMA）系统的Rényi熵。输出过程的特征函数由其残差特征函数的各项表示。推导出了计算MCARMA系统输出过程Rényi熵的显式公式。此外，我们研究了协方差矩阵以找到Rényi熵的上界。我们进行了三次仿真，用以说明MCARMA系统中信息的行为，其中控制项和噪声分别服从高斯、柯西和拉普拉斯分布。最后，在两个实际应用中展示了Rényi熵的行为：一个造纸过程和一个电路系统。
英文摘要：
Rényi entropy is an important measure in the context of information theory as a generalization of Shannon entropy. This information measure was often used for uncertainty quantification of dynamical behaviour of stochastic processes. In this paper, we study in detail this measure for multivariate controlled autoregressive moving average (MCARMA) systems. The characteristic function of output process is represented from the terms of its residual characteristic function. An explicit formula to compute the Rényi entropy for the output process of MCARMA system is derived. In addition, we investigate the covariance matrix to find the upper bound of Rényi entropy. We present three simulations that serve to illustrate the behavior of information in MCARMA system, where the control and noise follow the Gaussian, Cauchy and Laplace distributions. Finally, the behaviour of Rényi entropy is illustrated in two real-world applications: a paper-making process and an electric circuit system.
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