DOI: https://doi.org/10.24144/2616-7700.2020.2(37).%p

Напрямки наукових дослiджень Ю.В. Козаченка: статистичне моделювання

А. О. Пашко, I. В. Розора, О. I. Василик

Анотація


В роботi висвiтлюються науковi здобутки доктора фiзико-математичних наук професора Юрiя Васильовича Козаченка в галузi статистичного моделювання. Козаченко Ю.В. працював на кафедрi теорiї ймовiрностей, статистики та актуарної математики КНУ iменi Тараса Шевченка. Професор Козаченко Ю.В. стояв бiля витокiв статистичного моделювання в Київському унiверситетi. Козаченко Ю.В. та його учнями розробленi науковi основи теорiї моделювання гауссових та близьких до них випадкових процесiв i полiв в рiзних функцiональних просторах iз заданими точнiстю i надiйнiстю. При розробцi методiв статистичного моделювання значна увага придiлялась дослiдженню збiжностi статистичних моделей випадкових процесiв та полiв в рiзних функцiональних просторах. До результатiв наукової школи Козаченка Ю.В. належить i розробка теорiї функцiональних просторiв випадкових величин. Значне мiсце в цих дослiдженнях займають простори Орлiча.

Ключові слова


субгауссовi процеси; простори Орлiча; статистичне моделювання; точнiсть; надiйнiсть

Посилання


Zelepugina, I.P., & Kozachenko, Yu.V. (1982). On the question of the simulation of Gaussian stochastic processes Some questions of the theory of stochastic processes, Collect. sci. Work. (pp. 47–56). Kiev. [in Russian]

Kozachenko, Yu.V., & Pashko, A.A. (1988). Modeling the Gaussian stationary stochastic processes representable in the form of stochastic integrals. Theory and applications of statistical modelling, Collect. Sci. Works. (pp. 10–24). Novosibirsk.[in Russian]

Zelepugina, I.N., & Kozachenko, Yu.V. (1988). On accuracy estimations in modelling random fields in spaces Lp, p > 1. Issled. Oper. ASU. 32. 10–14.[in Russian]

Donchenko, V.S. (1982). Simulation of L2 – processes. Dopov. Akad. Nauk Ukr. RSR. 5. 60–62. [in Ukrainian]

Yadrenko, M.Y., & Rahimov, G.K. (1993). Statistical simulation homogeneous and isotropic field on plane. Theor. Probability and Math. Statist. 49. 245–251.[in Russian]

Yadrenko, M.Y., Yadrenko, O.M., & Grikh, Z.O. (1993). About Approximation and Statistical Simulation of Izotropic Fields. Random Operators and Stochastic Equations. 1, 1. 37–45.

Buldygin, V.V., & Kozachenko, Yu. V. (1988). Metric characterization of random variables and random processes. K.: TViMS. [in Russian]

Kozachenko, Yu. V., & Pashko, A.O.(1999). Simulation of random processes. K.: Kyiv University Publishing House. [in Ukrainian]

Buldygin, V.V.,& Kozachenko, Yu.V. (2000). Metric characterization of random variables and random processes. Translations of Mathematical Monographs. 188. Providence, RI: AMS, American Mathematical Society. xii.

Kozachenko, Yu.V., Pashko, A.O., & Rozora, I.V. (2007). Simulation of random processes and fields. K.: Zadruga. [in Ukrainian]

Vasylyk, O.I., Kozachenko, Yu.V., & Yamnenko, R.E. (2008). ϕ - suggaussian random processes. K.: Kyiv University Publishing House. [in Ukrainian]

Kozachenko, Yu.V., Pogorilyak, O.O., & Tegza, A.M. (2012). Simulation of random processes and Kox–processes. Uzgorod: Karpaty. [in Ukrainian]

Kozachenko, Yu., Pogoriliak, O., Rozora, I., & Tegza, A. (2016). Simulation of Stochastic processes with given accuracy and reliability. London: ISTE Press Ltd, Elsevier Ltd.

Kozachenko, Yu.V., & Pashko, A.O. (2016). Accuracy and reliability of simulation of random processes and fields in uniform methrics. K: TOV SIK GROUP Ukraine. [in Ukrainian]

Kozachenko, Yu.V.,& Pashko, A.A. (1999). Accuracy of simulation of stochastic processes in norms of Orlicz spaces.I. Theor. Probability and Math. Statist. 58. 51–66. [in Ukrainian]

Kozachenko, Yu.V.,& Pashko, A.A. (1999). Accuracy of simulation of stochastic processes in norms of Orlicz spaces.II. Theor. Probability and Math. Statist. 59. 77–92. [in Ukrainian]

Kozachenko, Yu.V., & Kozachenko, L.F. (1991). Accuracy of modeling stationary Gaussian stochastic processes in L2(0 T). Vychisl. Prikl. Mat. 75. 108–115. [in Ukrainian]

Kozachenko, Yu.V., & Kozachenko, L.F. (1992). On accuracy of modeling of Gaussian stochastic processes in L2(0 T). Vychisl. Prikl. Mat. 74. 88–93. [in Ukrainian]

Kozachenko, Yu.V., & Kozachenko, L.F. (1992). On the modelling of Gaussian stationary processes with absolutely continuous spectrum. Teor. Jmovirn. Mat. Stat. 47. 47–54. [in Ukrainian]

Kozachenko, Yu.V., Pashko, A.O., & Zelepugina, I.M. (2001). The accuracy of simulation of sub-Gaussian random fields in some functional spaces. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky. 1. 11–17. [in Ukrainian]

Kozachenko, Yu.V., & Pashko, A.A. (2000). On the simulation of random fields.I. Theor. Probability and Math. Statist. 61. 61–74. [in Ukrainian]

Kozachenko, Yu.V., & Pashko, A.A. (2001). On the simulation of random fields.II. Theor. Probability and Math. Statist. 62. 51–63. [in Ukrainian]

Kozachenko, Yu.V., & Pashko, A.O. (2002). Estimation of accuracy of simulation of random fields on the sphere in Lp, p ≥ 2. Visn., Mat. Mekh., Kyiv. Univ. Im. Tarasa Shevchenka. No.7–8. 26–32. [in Ukrainian]

Kozachenko, Yu.V., & Pashko, A.O. (2013). The estimation of the speed of the models of the sub-Gaussian random processes in the Orliz space. it Development of the National Academy of Sciences of the Republic of Kazakhstan. Type of physical-mathematical. No6(292). 60–65.[in

Russian]

Kozachenko, Yu.V., & Rozora, I.V. (2004). Accuracy and reliability of models of stochastic processes of the space Subϕ(Ω). Teor. Jmovirn. Mat. Stat. 71. 93–104.

Kozachenko, Yu.V., & Rozora, I.V. (2004). On simulation of stochastic processes from the space Subϕ(Ω). Prykl. Stat., Aktuarna Finans. Mat. 1.72–78.

Kozachenko, Yu.V., & Vasylyk, O.I. (1998). On the distribution of suprema of Subϕ(Ω) random processes. Theory of Stochastic Processes. 4(20), No1-2. 147–160.

Kozachenko, Yu.V., & Rozora, I.V. (2003). Simulation of Gaussian stochastic processes. Random Operators and Stochastic Equations. 11, No3. 275–296.

Kozachenko, Yu.V., & Rozora, I.V. (2004). Simulation of Gaussian Stochastic Fields. Theory of Stochastic Processes. 10(26), No.1-2. 48–60.

Kozachenko, Yu.V., & Rozora, I.V. (2006). Application of the theory of Square-Gaussian Processes to simulation of Stochastic Processes. Theory of Stochastic Processes. 12(28), No3- 4. 43–54.

Kozachenko, Yu.V., & Pashko, A.A. (2014). Accuracy of Simulation of the Gaussian random processes with continuous spectrum. Computer Modelling and New Technologies. 18, No 3.7–12.

Antonini, R.G., Kozachenko, Yu.V., & Tegza, A.M. (2002). Accuracy of simulation in Lp od Gaussian random processes. Bulletin of the University of Kiev. Series: Physics & Mathematik. 5. 7–14. [in Ukrainian]

Antonini, R.G., Kozachenko, Yu.V., & Sorokulov, V.V. (2003). On accuracy and reliability of simulation of some random processes from the space Subϕ(Ω). Theory of Stochastic Processes. 9(25), No3-4. 50–57.

Kozachenko, Yu.V., Sottinen, T., & Vasylyk, O.I. (2005). Simulation of weakly self–similar stationary increment Subϕ(Ω) –processes: a serias expansion approach. Methodology and Computing in Applied Probability. 7, No3. 379–400.

Kozachenko, Yu., Vasylyk, O., & Pashko, A. (2018). Simulation of generalized fractional Brownion motion in C([0, T]). Monte Carlo Methods and Applications. 24, Iss.3. 179–192.

Kozachenko, Yu., Vasylyk, O., & Pashko, A. (2017). Simulation of generalized fractional Brownion motion in Lp([0, T]). Teor. Jmovirn. Mat. Stat. 97. 97–108. [in Ukrainian]

Pashko, A.A. (2014). Simulations of standart Brownian motion. Computer modelling and new Technologies. 18, No10. 516–521.

Kahane, J.P. (1960). Propri’et’es locales des fonctions ‘a series de Fouries al’eatories. Studia Math. 19, No 1. 1–25.

Kozachenko, Yu.V. (1968). Sufficient conditions of continuity with unity probability of subgaussian random processes. Dopov. Akad. Nauk Ukr. RSR, Ser. A. 2. 113–115. [in Ukrainian]

Buldygin, V.V., & Kozachenko, Yu.V. (1980). Sub-Gaussian random variables. Ukr. Mat. Zh. 32. 723–730. [in Ukrainian]

Buldygin, V.V., & Kozachenko, Yu.V. (1987). Subgaussian random vectors and processes. Teor. Veroyatn. Mat. Stat. 36. 10–22.[in Russian]

Buldygin, V.V., & Kozachenko, Yu.V. (1993). Estimates of the supremum distribution for a certain class of random processes. Ukr. Mat. Zh. 45, No.5.596–608. [in Ukrainian]

Kozachenko, Yu.V., & Ostrovskij, E.I. (1985). Banach spaces of random variables of subGaussian type. Teor. Veroyatn. Mat. Stat. 32. 42–53. [in Russian]

Pashko, A.A. (1989). Computer simulation of Gaussian stationary random processes during testing of agricultural machines. System test methods for livestock and forage production. Collection of scientific papers VNIIMOZH. Novokubansk. 7–14.[in Russian]

Pashko, A.A. (1990). Mathematical and software support for digital methods of analysis of random processes in information-measuring systems for the automation of bench tests. New in test methods for agricultural machinery. Collection of scientific papers VNIIMOZH. Novokubansk. 19–28. [in Russian]

Pashko, A.O. (2017). Simulation of telecommunication traffic using statistical models of fractional Brownian motion. 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T). 414–418. doi: 10.1109/INFOCOMMST.2017.8246429.

Pashko, A.O., Rozora, I.V. (2018). Accuracy of simulation for the network traffic in the form of fractional Brownian motion. 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET). 840–845. doi: 10.1109/TCSET.2018.8336328.

Pashko A., Vasylyk O. (2019). Statistical Simulation of Size Behavior for TCP Windows. IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S&T). 617–620. doi:10.1109/PICST47496.2019.9061332.

Pashko, A.O., Lukovych, O.V., Rozora, I.V., Oleshko, T.A., & Vasylyk, O.I. (2019). Analysis of simulation methods for fractional Brownian motion in the problems of intelligent systems design. IEEE International Conference on Advanced Trends in Information Theory. 373–378. doi: 10.1109/ATIT49449.2019.9030478.


Посилання

  • Поки немає зовнішніх посилань.


Copyright (c) 2020 А. О. Пашко