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Mathematical models and analysis of stochastic oscillations

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PL
Modele matematyczne i analiza oscylacji stochastycznych
Języki publikacji
EN
Abstrakty
EN
Description of the properties of stochastic oscillation in terms of probabilistic characteristics of the periodically correlated stochastic processes and their generalizations is presented. General approach to the problems of estimation of these characteristics on the basis of natural data is considered, possible estimation methods are analyzed and the results of investigation of hidden periodicities are given.
PL
W pracy przedstawiono właściwości oscylacji stochastycznych przy wykorzystaniu charakterystyk probabilistycznych okresowo skorelowanych procesów stochastycznych i ich uogólnień. Zaprezentowano ogólne podejście do problemów estymacji powyższych charakterystyk na bazie tzw. danych naturalnych. Przeanalizowano również możliwe do zastosowań metody estymacji oraz wyniki badań dotyczących znajdywania ukrytych okresowości.
Twórcy
  • Institute of' Telecommunication. University of Technology and Life Sciences. Bydgoszcz, Poland Karpenko Physic-Mechanical Institute of National Academy of Sciences of Ukraine. Lviv
Bibliografia
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  • [7] Mikhailyshyn V., Fligel S., Javors'kyj I., 1990. Statistical analysis of wave packets of geomagnetic pulsations Pel type by the method of periodically correlated random processes. Geomagnetizm i Aeronomia 30(5), 757-764 (in Russian).
  • [8] Karmalita V.. 1986. The digital processing of the random oscillations. Mashinostroenie Moscow (in Russian).
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  • [34] Dragan Ya., Javors'kyj L, 1975. About representation of sea waves by periodically correlated random processes and their statistical processing methods. Methods of Representation and Apparatus Analysis of Random Processes and Fields. XIII Ail-Union Symposium. Leningrad, 29-33 (in Russian).
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  • [38] Mamontov N., 1968. The investigation of distribution statistics of the relative air humidity. Trudy NIIAK 54, 18-28 (in Russian).
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  • [42] Groisman P., 1977. The estimate of autocorrelation matrixes of the precipitation time series considered as periodically correlated random processes. Trudy GGL 247, 119-127 (in Russian).
  • [43] Dragan Ya., Javors'kyj L, 1975. About description of sea wave rhythmic. Proc. of VI All-Union Workshop on Statistical Hydroacoustics, Novosibirsk, 197-206 (in Russian).
  • [44] Dragan Ya., Javors'kyj L, 1977. The description of sea wave rhythmic. Visnyk AN USSR 2, 26-36 (in Russian).
  • [45] Javors'kyj L, 1978. The investigation of rhythmic of sea waves and their influence on transfer of underwater acoustic signals. Cand. Phys. and Math. Sci. Dissertation. Far-Eastern Scientific Centre of AN USSR, Vladivostok (in Russian).
  • [46] Javors'kyj L, 1978. The estimates of probabilistic characteristics of sea waves considered as periodically correlated random processes. Ail-Union Institute of Scientific and Technical Information Moscow.
  • [47] Dragan Ya., Javors'kyj L. 1980. Statistical processing of space and time signals with rhythmic structure. Signal Spacetime Processing Voronezh: Vor. State University, 77-85 (in Russian).
  • [48] Dragan Ya., Mezentsev V., Javors'kyj I., 1980. The problem of verification of stochastic rhythmic model. Otbor Peredacha Informatsiyi 59, 3-12 (in Russian).
  • [49] Javors'kyj I., 1981. The problems of correlation analysis of periodically correlated random processes. Proc. of X All-Union Workshop on Statistical Hydroacoustics. Novosibirsk, 52-54 (in Russian).
  • [50] Dragan Ya., Mezentsev V., Javors'kyj I., 1981. The problems of spectral processing of rhythmic signals. Thesis of Report of XIII All-Union Conf. on Coding and Transfer of Information, P. IV, Moscow-Kuybyshev, 91-95 (in Russian).
  • [51] Dragan Ya., Javors'kyj 1., 1982. Rhythmic of Sea Waving and Underwater Acoustic Signals. Naukova Dumka Kyiv (in Russian).
  • [52] Javors'kyj I., 1984. The properties of mean and correlation function estimates of periodically correlated random processes. Otbor i Peredacha Informatsiyi 67, 22-28 (in Russian).
  • [53] Dragan Ya., Mezentsev V., Javors'kyj 1., 1984. The computation of the spectral characteristic estimates of periodically correlated random processes. Otbor i Peredacha Informatsiyi 69, 29-35 (in Russian).
  • [54] Dragan Ya., Rozhkov V., Javors'kyj I., 1984. The application of methods of periodically correlated random processes theory for probabilistic analysis of oceanological time series. Probabilistic Analysis and Modelling of Oceanological Processes. Gidrometeoizdat Leningrad, 4-23 (in Russian).
  • [55] Javors'kyj I., 1984. The application of Buys-Ballot scheme for statistical analysis of rhythmical signals. Izvestiya Vysshykh Uchebnykh Zavedenij, ser. Radioelektronica 27(11), 31-37 (in Russian).
  • [56] Rozhkov V., Trapeznikov Yu., Javors'kyj I.. 1984. Statistical analysis of seasonal survey data. Proc. XIV Conf. Baltic Oceanogr. - Gdynia, Polish Academy of Sciences, 370-374.
  • [57] Javors'kyj I., 1985. The component sample estimates of probabilistic characteristics of periodically correlated random processes. Otbor i Peredacha Informatsiyi 72, 17-27 (in Russian).
  • [58] Javors'kyj I.. 1985. On statistical analysis of periodically correlated random processes. Radiotekhnika i Electronika 6, ! 096-1104 (in Russian).
  • [59] Javors'kyj I., 1985. The computation of characteristics of periodically correlated random processes by data random selection. Thesis of Reports of I Acoustical Seminar on Modelling, Algorithms and Reception of Decision, Moscow, 44-49 (in Russian).
  • [60] Javors'kyj L, 1986. Statistical analysis of biperiodically correlated random processes. Otbor i Peredacha Informatsiyi 73, 12-21 (in Russian).
  • [61] Javors'kyj I., 1986,On period estimate of periodically correlated random processes Otbor i Peredacha Informatsiyi 74, 6-13 (in Russian).
  • [62] Dragan Ya., Javors'kyj I., 1986. On characteristics of the system for analysis of periodically correlated random processes. Statistical Processing of Experimental Data, Novosibirsk Electro-tekhnical Inst., 53-58 (in Russian).
  • [63] Javors'kyj L, 1986. The component estimates of probabilistic characteristics of periodically correlated random processes. Avtomatika 4, 44-48 (in Russian).
  • [64] Javors'kyj I., 1987. The statistical analysis of vector periodically correlated random processes. Otbor i Peredacha Informatsiyi 76, 3-12 (in Russian).
  • [65] Javors'kyj I., 1987. The interpolation of the estimates of periodically correlated random processes. Avtomatika 1, 36-41 (in Russian).
  • [66] Kostjukov Ya., Mezentsev V.. Uljanich I., Javors'kyj I., 1987. The analysis of nonequidistant time series of Gulf of Riga water temperature and salinity. Proc. of Ail-Union Scientific Research Institute of Hydrometeorological Information - World Data Centre 139, 87-97 (in Russian).
  • [67] Javors'kyj I., 1987. Biperiodically correlated random processes as model of bi-rhythmic signals. All-Union Conf. on Information Acoustics, Moscow, 6-10 (in Russian).
  • [68] Mezentsev V., Javors'kyj I., 1984. The estimation of rhythmic signal probabilistic characteristics as a problem of linear filtration. Izvestia Vysshykh Uchebnykh Zavedenij. ser. Radioelectronika 27(11). 3 1-37 (in Russian).
  • [69] Javors'kyj I., 1988. The statistical properties of biperiodically correlated random processes sample sequences. Otbor i Obrabotka Informatsiyi 1(77), 16-23 (in Russian).
  • [70] Mezentsev V., Javors'kyj L, 1988. The properties of the optimum estimates of rhythmic signal probabilistic characteristics. Thesis of the Reports of All-Union Workshop On Signal Processing, Uljanovsk Polytechnical Institute, !6-18 (in Russian).
  • [71] Javors'kyj I., 1988. The methods of statistical analysis of periodically correlated and allied random processes and their application in oceanology. Perspective Methods of Experimental Planning and Analysis for Investigation of Random Processes and Fields, Moscow, 102-103 (in Russian).
  • [72] Javors'kyj I., 1988. The least squares method for statistical analysis of signals with rhythmical structure. II All-Union Acoustical Seminar on Modelling, Algorithms and Reception of Decisions, Moscow, 5-6 (in Russian).
  • [73] Kostjukov Ya., Mezentsev V., Uljanich I., Javors'kyj I., 1988. The annual cycle structure of the temperature, salinity and level time series at the shore station of the Gulf of Riga. The Regime-forming Factors. Hydrometeorological and Hydro-chemical Processes on USSR Seas., Gidrometeoizdat Leningrad, 113-124 (in Russian).
  • [74] Mjakisheva N., Rozhkov V., Uljanich I., Javors'kyj I., 1989. The estimates of probabilistic characteristics of hydrometeorological processes annual and diurnal changeability. The Regime-forming Factors. Information Base and Methods of its Analysis, Gidrometeoizdat Leningrad, 47-77 (in Russian).
  • [75] Rozhkov V., Chemyshov S., Trapeznikov Ya., Javors'kyj I., 1989. The comparison of the probabilistic characteristics estimation methods of the oceanological process annual changeability. The Regime-forming Factors, Information Base and Methods of its Analysis. Gidrometeoizdat Leningrad, 138-149 (in Russian).
  • [76] Javors'kyj I., 1989. The statistical analysis methods of the oceanological process rhythmics. Dokt. Phys. and Math. Sci. Dissertation, Arctic and Antarctic Institute Leningrad (in Russian).
  • [77] Javors'kyj 1., 1989. Statistical analysis of poly- and almost periodically correlated random processes. Otbor i Obrabotka Enformatsiyi 3(79), 3-10 (in Russian).
  • [78] Mikhaiiyshyn V., Javors'kyj I., 1990. LSM-ana!ysis while identifying poly-rhythmic structure of stochastic signals. Proc. of the First Intern. Conf. on Information Technologies for Image Analysis and Pattern Recognition, Lviv, 321-325.
  • [79] Mikhaiiyshyn V., Javors'kyj I., 1991. Probabilistic model of oceanological process rhythmic and its analysis methods. Perspective Methods of Experimental Planning and Analysis for Investigation of Random Processes and Fields, Moscow, 24-25 (in Russian).
  • [80] Mikhaiiyshyn V., Javors'kyj I., 1992. The hidden periodicities: models, detecting, analysis. Probabilistic Models and Processing of the Random Signals and Fields. Kharkiv, 107-110 (in Ukrainian).
  • [81] Panasjuk O., Javors'kyj I., 1992. The properties of periodically correlated random process spectral characteristic estimates by coherent analysis. Ibid., 111-114 (in Ukrainian).
  • [82] Mikhailyshyn V., Javors'kyj 1., 1992. Parametric models of stochastic oscillations and their statistical processing methods. Signal and Image Processing and Pattern Recognition. Proc. of the First All-Ukrainian Conf., Kyiv, 52-54 (in Ukrainian).
  • [83] Mikhailyshyn V., 1992. The statistical methods of hidden periodicities detecting and their application for analysis of geomagnetic pulsation oscillation structure. Cand. Phys. and Math. Sci. Dissertation, Lviv State University (in Russian).
  • [84] Mikhailyshyn V., Javors'kyj I., 1994. The probabilistic structure of the season variability of air temperature. Meteorologia i Hydrologia 2, 20-35 (in Russian).
  • [85] Panasyuk O., Javors'kyj I., 1994. Spectral analysis of signals with stochastic recurrence. Izvestia Vysshykh Uchebnykh Zavedeniy, ser. Radioelektronika 37(12), 47-57 (in Russian).
  • [86] Isayev I., Javors'kyj I., 1995. Component analysis of the time series with rhythmical structure. Izvestia Vysshykh Uchebnykh Zavedeniy, ser. Radioelektronika 38(1), 34-45 (in Russian).
  • [87] Mikhailyshyn V., Javors'kyj 1., 1993. The component estimation of the period of stochastic recurrence of rhythmical signals. Avtomatika 4, 44-48 (in Russian).
  • [88] Mikhailyshyn V., Fligel D., Javors'kyj [., 1990. The probabilistic model of the signals periodicity of geomagnetic pulsation Pel. Investigation of structure and wave properties near-earth plasma. Nauka Moscow, 76-88 (in Russian).
  • [89] Mikhailyshyn V.. Javors'kyj I., 1996. Modulated non-stationary random process. Dopovidi NAN Ukrainy 2, 70-74 (in Ukrainian).
  • [90] Javors'kyj I., Mikhailyshyn V., 1996. Probabilistic models and investigation of hidden periodicities. Appl. Math. Lett. 9(2), 21-23.
  • [91] Javors'kyj I., Mikhailishin V., 1996. Probabilistic models and statistical analysis of stochastic oscillations. Pattern Recognition and Image Analysis 6(4), 749-763.
  • [92] Isayev I., Javors'kyj I., 1996. Component spectral analysis of signals with stochastic recurrence. Problemy Upravlenia i Informatiki 4, 104-113 (in Russian).
  • [93] Panasyuk O., Javors'kyj I., 1996. Properties of spectral component estimates of periodically correlated random processes. Elektronnoe Modelirovanie 18(2), 17-24 (in Russian).
  • [94] Mikhailyshyn V., Javors'kyj I., 1996. Statistical analysis of radiophysical processes with hidden periodicity. Radiofizika i Radioastronomia 2, 243-254 (in Russian).
  • [95] Javors'kyj I., Mikhailyshyn V., 1996. Probabilistic analysis of electromagnetic phenomena with stochastic periodicity. Proc. of VI Intern. Conf. on Mathematical Methods in Electromagnetic Theory, Lviv, 252-255 (in Ukrainian).
  • [96] Javors'kyj I., Mikhailyshyn V., 1996. Detecting of hidden periodicities of time series generated by non-linear processes in magnetoplazma. Ibid., 596-605 (in Russian).
  • [97] Mikhailyshyn V., Javors'kyj I., 1997. Narrow-band non-slationary random processes. Radiotekhnika i Elektronika 42(5), 596-605 (in Russian).
  • [98] Panasyuk O., Javors'kyj I., Karpenko G., 1997. Properties of spectral component estimates in periodically correlated random processes. Engineering Simulation 14, 191-204.
  • [99] Mikhailyshyn V.. Javors'kyj I., Vasilina Yu., Drabich O., Isayev I. Probabilistic models and statistical methods of vibration signal analysis for machine and constructor diagnostics. Fizyko-Khimichna Mekhanika Materially 5, 61-74 (in Ukrainian).
  • [100] Panasyuk O., Javors'kyj I., 1997. Coherent spectral analysis on time series with periodical probabilistic structure. Izvestia Vysshykh Uchebnych Zavedenij, ser. Radioelektronika40(8), 51-59 (in Russian).
  • [101] Isayev I., Javors'kyj I., 1998. Spectral analysis of time series with rhythmical structure. Problemy Upravlenia i Informatiki 2, 115-122 (in Russian).
  • [102] Javors'kyj I., Drzycimski Z.. Majewski J., Zakrzewski Z., 1998. Correlation and spectral properties of non-stationary modulated signals. Kwartalnik Elektrotechniki i Elektroniki 2. 21-50 (in Polish).
  • [103] Javors'kyj I., Zakrzewski Z.. 1998. Coherent analysis of non-stationary amplitude modulated signals. Otbor i Peredacha Informacii 12(88), 71-76 (in Ukrainian).
  • [104] Drabych O., Mykhaj lyshyn V., Javors'kyj I., 1999. Detection of regular periodical changes of signal and their periods estimation. Vidbir i Obrobka Informatsiji 13(89), 26-31 (in Ukrainian).
  • [105] Javors'kyj 1., Isayev I.. Majewski J., 1999. The properties of component estimators of non-stationary amplitude modulated signal characteristics. Vidbir i Obrobka Informatsiji 13(89), 32-37 (in Ukrainian).
  • [106] Javors'kyj 1., Zakrzewski Z., 2000. Coherent covariance analysis of non-stationary modulated signals. Kwartalnik Elektroniki i Telekomunikacji 46(3), 355--400 (in Poland).
  • [107] Zabolotnyj O., Mykhajlyshyn V., Javors'kyj I., 2000. The least squares method of polyrhythmic statistical analysis. Dopovidi NAN Ukrainy 8, 93-100 (in Ukrainian).
  • [108] Javors'kyj I., Isayev 1., Majewski J., 2000. The properties of discrete component estimator characteristics of non-stationary modulated signals. Vidbir 1 Obrobka Informatsiji 14(90). 41-46 (in Ukrainian).
  • [109] Drabych O., Mykhajlyshyn V.. Javors'kyj I., 2000. Determination of correlation period of the periodically correlated random processes using covariation transformations. Vidbir i Obrobka Informatsiji 14(90), 47-52 (in Ukrainian).
  • [110] Javors'kyj 1., Mykhajlyshyn V., 2001. Mathematical models, detection and analysis of hidden periodicities. Vidbir i Obrobka Informatsiji 15(91), 87-95 (in Ukrainian).
  • [111] Zabolotnyj O., Mykhajlyshyn V.. Javors'kyj I., 2002. The likelihood estimate analysis of probability characteristics of signal with polyrhythmic structure. Vidbir i Obrobka Informatsiji 16(92), 47-52 (in Ukrainian).
  • [112] Zabolotnyj O., Mykhajlyshyn V., Javors'kyj I., 2002. Mean estimate of polyrhythmic time series by the least squares method. Vidbir i Obrobka Informatsiji. 17(93), 65-70 (in Ukrainian).
  • [113] Javors'kyj I., Mykhajlyshyn V., Zabolotnyj O.. 2003. Least Squares Method in Statistical Analysis of Polyrythmics. Appl. Math. Let. 16, 1217-1222.
  • [114] Zabolotnyj O., Mykhajlyshyn V.. Javors'kyj I., 2004. The least squares of probabilistic characteristics of polyrhythmic signals. Izvestija Vysshykh Uchebnych Zavedenij, ser. Radioelektronika 8, 67-75 (in Russian).
  • [115] Isayev I., Kravets I., Javors'kyj I., 2004. To parametric modelling of periodically correlated random processes. Vidbir i Obrobka Informatsiji, 21(97), 11-165 (in Ukrainian).
  • [116] Gruza G., 1982. Some general problems of time series statistical analysis in climatology. Proc. of Ail-Union Scientific Research Institute of Hydrometeorologi-cal Information - World Data Centre 83, 3-9 (in Russian).
  • [117] Poljak I., 1978. Methods of Analysis of Random Processes and Fields in Climatology. Gidrometeoizdat Leningrad (in Russian).
  • [118] Bjelyshev A., Klevantsov Yu., Rozhkov V., 1983. Probabilistic analysis of sea currents. Gidrometeoizdat Leningrad (in Russian).
  • [119] Gudzenko L., 1961. The generalization of the ergodic theorem for nonstationary random processes. Izvestia Vysshikh Uchebnykh Zavedenij, ser. Radiofizika IV(2), 265-274 (in Russian).
  • [120] Serebrjennikov M., Pervozvansky A., 1965. The hidden periodicities detecting. Nauka Moscow (in Russian).
  • [121] Yaglom A., 1981. Correlation theory of stationary random functions. Gidrometeoizdat Leningrad (in Russian
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT1-0029-0004
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