Correlation properties of the random linear high-order Markov chains
TL;DR: The aim of this paper is to study the correlation properties of random sequences with additive linear conditional probability distribution function (CPDF) and elaborate a reliable tool for their generation.
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Abstract: The aim of this paper is to study the correlation properties of random sequences with additive linear conditional probability distribution function (CPDF) and elaborate a reliable tool for their generation. It is supposed that the state space of the sequence under examination belongs to a finite set of real numbers. The CPDF is assumed to be additive and linear with respect to the values of the random variable. We derive the equations that relate the correlation functions of the sequence to the memory function coefficients, which determine the CPDF. The obtained analytical solutions for the equations connecting the memory and correlation functions are compared with the results of numerical simulation. Examples of possible correlation scenarios in the high-order additive linear chains are given.
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Citations
Set pair prediction for Chinese natural gas energy security based on higher-order Markov chain with risk attitude
TL;DR: Wang et al. as discussed by the authors proposed a comprehensive evaluation criteria system, including four dimensions and eight indicators, and constructed an evaluation and prediction model based on set pair analysis, variable weight and high-order Markov chain.
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Correlation function inadequacy in random-sequence entropy measures.
TL;DR: This work derives the conditional entropy of the additive Markov chain as a sum of the Kullback-Leibler mutual information and gives an example of random sequence with the exactly zero correlation function and the nonzero correlations.
Two-Point Probability Functions and Correlation Properties of the Generalized Additive High-Order Markov Chains
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- 26 Aug 2021
TL;DR: In this paper, the authors studied statistical properties of finite state Markov chains of the Nth order and obtained analytical solutions for the stationary probability distribution vector and for the correlation matrix and, thus, for the two-point probability distribution functions of the chain.
References
Book Review: Introduction to Information Retrieval by Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schütze
Olga Vechtomova
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