微分护送变换与LMC -Rényi复杂性测度的单调性
Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure
摘要：
Escort分布在信息论、非广延统计力学、编码理论、混沌和多重分形等诸多领域都有着重要的应用。在这项工作中，我们给出了一种新类型的护送密度的概念和性质，差分护送密度，它具有各种优势，相对于标准的。我们突出的行为的微分香农，雷尼和Tsallis熵这些分布。然后，我们说明了他们的效用证明的单调性性质的LMC-Rényi复杂性测度和研究的行为一般分布在两个极端情况下的最小和非常高的LMC-Rényi复杂性。最后，这种变换使我们能够获得Tsallis q-指数密度作为指数密度的微分护送变换。
英文摘要：
Escort distributions have been shown to be very useful in a great variety of fields ranging from information theory, nonextensive statistical mechanics till coding theory, chaos and multifractals. In this work we give the notion and the properties of a novel type of escort density, the differential-escort densities, which have various advantages with respect to the standard ones. We highlight the behavior of the differential Shannon, Rényi and Tsallis entropies of these distributions. Then, we illustrate their utility to prove the monotonicity property of the LMC-Rényi complexity measure and to study the behavior of general distributions in the two extreme cases of minimal and very high LMC-Rényi complexity. Finally, this transformation allows us to obtain the Tsallis q-exponential densities as the differential-escort transformation of the exponential density.
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