Memory functions and Correlations in Additive Binary Markov Chains

Details Memory functions and Correlations in Additive Binary Markov Chains Memory functions and Correlations in Additive Binary Markov Chains

2006-03-21

arxiv.org/abs/physics/0603171v1

Physics

Data Analysis, Statistics and Probability

11 pages, 5 figures

Scientific paper

10.1088/0305-4470/39/46/004

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.

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