Abstract
The limitations of the Shannon entropy and the dynamic Shannon entropy are discussed. They only measure the aleatory uncertainty of stochastic processes. In this paper, based on the practical considerations, an entropy formula for measuring the uncertainty of stochastic processes is proposed, which measures not only the aleatory uncertainty but also the epistemic uncertainty. The uncertainty of the Gaussian process in four different situations is discussed. These works fill the gap between information theory and signal processing and thus can be used as a design guideline for constructing a secure source in the security field.
Highlights
The stochastic process is divided into stationary process and non-stationary process.1 The statistical properties, such as mean and variance, of the stationary process are time-invariant
Based on the Shannon entropy,23 a stochastic process with the maximum entropy (ME) will do better in improving system security because the uncertainty of this stochastic process is maximum in this case
A stationary process with the ME is a better choice for system security from the perspective of information theory
Summary
The stochastic process is divided into stationary process and non-stationary process.1 The statistical properties, such as mean and variance, of the stationary process are time-invariant. In this paper, based on the practical considerations, an entropy formula for measuring the uncertainty of stochastic processes is proposed, which measures the aleatory uncertainty and the epistemic uncertainty. The Shannon entropy is based on a stationary assumption that the probability density function (PDF) of the stochastic process is time-invariant.
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