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ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

SYMBOLIC MARKOV CHAINS WITH MULTILINEAR MEMORY FUNCTION

heading: 
STATISTICAL RADIOPHYSICS
Melnyk, SS, Usatenko, OV
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: olegusatenko@mail.ru
https://doi.org/10.15407/rej2015.03.079
Language: russian
Abstract: 

The problem of designing various radio devices, such as filters, delay lines, random antennas with a given radiation pattern and so on, requires the development of methods for constructing random sequences of the parameters of these systems having specified correlation properties. An adequate mathematical approach for solving such problems is the Markov chains of higher orders. Statistical characteristics of these objects are completely determined by their conditional probability function that, in general, can be very complicated. The purpose of this paper is to present the decomposition procedure for the conditional probability function of random sequences with long-range correlationtions in a form convenient for their numerical generation. Here we restrict ourselves to the case of the state space of the system of such kind, when random values of its elements belong to the finite abstract set. The developed theory opens the way to build a more consistent and nuanced approach for the description of systems with long-range correlations. In the limiting case of weak (by value, but not the distance) correlations memory function is uniquely expressed in terms of higher-order correlation functions, allowing us to generate a random sequence with a given long-range correlations. As an example of the analytical results obtained, which can be used in practical applications, we present an example of the numerical realization of the method of construction of random sequence with specified correlators of the second and third orders.
Keywords: correlation functions, random sequences, the function of conditional probability, the high order Markov chains

Manuscript submitted  09.07.2015 г.
PACS     05.40.-a; 07.05.Mh; 87.10.-e
Radiofiz. elektron. 2015, 20(3): 79-89
Full text  (PDF)

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