Memory functions of the additive Markov chains: applications to complex dynamic systems

A new object of the probability theory, the two-sided chain of symbols (introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties of binary multi-step Markov chains with the long-range correlations. Established statistical correspondence between the Markov chains and certain two-sided sequences allows us to prove the isotropy properties of three classes of the Markov chains. One of them is the important class of weakly correlated additive Markov chains, which turned out to be equivalent to the additive two-sided sequences.

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“…, N , is the memory function andā is the average number of unities in the sequence (see, e.g., Ref. [21]). …”

Section: General Definitionsmentioning

confidence: 99%

“…The concept of additive chains turned out to be very useful because it is possibile to evaluate the binary correlation function of the chain via the memory function (see for the details Refs. [20][21][22]). …”

Section: Introductionmentioning

confidence: 99%

Isotropy properties of the multi-step Markov symbolic sequences

Apostolov

Mayzelis

Usatenko

et al. 2007

Physica A: Statistical Mechanics and its Applications

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“…Such Markov chain is referred to as additive Markov chain, Ref. [29]. The homogeneity of the Markov chain is provided by the independence of the conditional probability Eq.…”

Section: A Basic Notionsmentioning

confidence: 99%

Memory functions and correlations in additive binary Markov chains

Melnyk

Usatenko

Yampol’skiı̆

et al. 2006

J. Phys. A: Math. Gen.

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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 for the analytically solvable model of the system with a step-wise memory function.

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“…Additive Markov chains are an efficient tool to simulate time series with long-range correlations because the transition probability can be expressed as a sum of functions, each depending on one of the previous states (memory functions). Strong analytic results exist for the case of binary time series [31][32][33][34]. In this case, the memory functions can be derived from the empirical autocorrelation function of the time series straightforwardly.…”

Section: Introductionmentioning

confidence: 99%

Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

2018

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Wind power generation exhibits a strong temporal variability, which is crucial for system integration in highly renewable power systems. Different methods exist to simulate wind power generation but they often cannot represent the crucial temporal fluctuations properly. We apply the concept of additive binary Markov chains to model a wind generation time series consisting of two states: periods of high and low wind generation. The only input parameter for this model is the empirical autocorrelation function. The two-state model is readily extended to stochastically reproduce the actual generation per period. To evaluate the additive binary Markov chain method, we introduce a coarse model of the electric power system to derive backup and storage needs. We find that the temporal correlations of wind power generation, the backup need as a function of the storage capacity, and the resting time distribution of high and low wind events for different shares of wind generation can be reconstructed.

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Memory functions of the additive Markov chains: applications to complex dynamic systems

Abstract: A new approach to describing correlation properties of complex dynamic systems with long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68, 061107 (2003)

Cited by 38 publications

References 16 publications

Isotropy properties of the multi-step Markov symbolic sequences

Isotropy properties of the multi-step Markov symbolic sequences

Memory functions and correlations in additive binary Markov chains

Modeling long correlation times using additive binary Markov chains: Applications to wind generation time series

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