Quality estimation for models of a generalized Wiener process

• Autorzy: Pashko Anatolii

Identyfikatory

DOI

10.15199/48.2020.10.16

Warianty tytułu

PL

Szacowanie jakości dla modeli uogólnionego procesu Wienera

• Języki publikacji: EN

Abstrakty

EN

In the paper, we study quality of statistical simulation of a generalized wiener process. In order to construct a model, we use spectral representation of a generalized Wiener process in the form of stochastic integral. The model is constructed with a given accuracy and reliability in the space of integrable functions. For estimation of the model quality we use estimates of the Hurst parameter, as well as estimates of correlation function of the increments of realizations obtained.

PL

W pracy badamy jakość statystycznej symulacji uogólnionego procesu Wienera. Do budowy modelu wykorzystujemy widmową reprezentację uogólnionego procesu Wienera, w postaci całki stochastycznej. Model budowany jest z określoną dokładnością i niezawodnością. Do oceny jakości modelu stosujemy oszacowania parametru Hursta oraz funkcji korelacji uzyskanych realizacji.

Słowa kluczowe

EN

generalized Wiener process; Hurst parameter; simulation of sub-Gaussian processes

PL

uogólniony proces Wienera; parametr Hursta; symulacja procesów sub-gaussowskich

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2020
• Tom: R. 96, nr 10
• Strony: 94--97
• Opis fizyczny: Bibliogr. 26 poz., rys.

Twórcy

autor

Pashko Anatolii

• Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, National Technical University of Ukraine “Igor Sikorsky Kyiv Politechnic Institute”, Kyiv, Ukraine

Bibliografia

• 1. Mishura Yu., Stochastic calculus for fractional Brownian motion and related processes,Springer, Berlin 2008.
• 2. Masaaki Kijima, Chun Ming Tam, Fractional Brownian Motions in Financial Models and Their Monte Carlo Simulation, INTECH: Theory and Applic. of Monte Carlo Simulations, (2013), 53-85.
• 3. Prigarin S., Hahn K., Winkler G., Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion, Siberian J. Num. Math., 2 (2008), 201-218.
• 4. Sabelfeld K., Monte Carlo Methods in Boundary Problems, Nauka, Novosibirsk 1989.
• 5. Norros I., A storage model with self-similar input, Queueing Systems, 16 (1984), 387-396.
• 6. Kilpi J., Norros I., Testing the Gaussian approximation of aggregate traffic, Proceedings of the second ACM SIGCOMM Workshop, Marseille, France, (2002), 49-61.
• 7. Pashko A., Simulation of Telecommunication Traffic Using Statistical Models of Fractional Brownian Motion, 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology. Conference Proceedings, (2017), 414-418.
• 8. Pashko A., Rozora I., Accuracy of simulation for the network traffic in the form of Fractional Brownian Motion, 14th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering, (2018), 840-845.
• 9. Dzhaparidze K.O., van Zanten J.H., A series expansion of fractional Brownian motion, CWI. Probability, Networks and Algorithms [PNA], R 0216 (2002).
• 10. Kozachenko Yu., Kamenshchikova O, Approximation of stochastic processes in the space Lp([0,T]), Theor. Probability and Math. Statist., 79 (2009), 83-88.
• 11. Pashko A., Statistical Simulation of the generalized Wiener process, Bulletin of Taras Shevchenko National University of Kyiv. Series Physics & Mathematics, 2 (2014), 180-183.
• 12. Nosova Y., Shushliapina N., Kostishyn S.V., Koval, L.G., et al., The use of statistical characteristics of measured signals to increasing the reliability of the rhinomanometric diagnosis, Proc. SPIE, 10031 (2016).
• 13. Smolarz A., Wojcik W., Gromaszek K., Fuzzy modeling for optical sensor for diagnostics of pulverized coal burner, 26th European Conference on Solid-State Transducers (Eurosensors), Krakow, Poland, (2012), Sep 09-12.
• 14. Kozachenko Yu., Pashko A., Vasylyk O., Simulation of generalized fractional Brownian motion in Lp([0,T]), Theor. Probability and Math. Statist., 97 (2018), 99-111.
• 15. Kozachenko Y., Pashko A., Vasylyk O., Simulation of generalized fractional Brownian motion in C([0,T]), Monte Carlo Methods and Applications, 24 (2018), n.3, 179-192.
• 16. Kurchenko O.O., One strong consistency estimate of the Hurst parameter of the fractional Brownian motion, Theory Probab. Math. Stat., 67 (2003), 97-106.
• 17. Zlepko S.M., Tymchyk S.V., Novikova A.O., Moskovko M.V., et al., An informational model of sportsman’s competitive activities, Proc. SPIE, 10031 (2016).
• 18. Smolarz A., Lytvynenko V., Wojcik W., et al., Multifractal spectra classification of flame luminosity waveforms, Proc. SPIE, 10808 (2018).
• 19. Kozachenko Yu., Kurchenko O., Sinyavska O., Levy-Baxter theorems for random fields and their applications, Shark, Uzhgorod 2018.
• 20. Kvyetnyy R., Bunyak Y., Sofina O., et al., Blur recognition using second fundamental form of image surface, Proc. SPIE 9816, (2015).
• 21. Kvyetnyy R., Romanyuk O., Titarchuk E.,et al., Usage of the hybrid encryption in a cloud instant messages exchange system, Proc. SPIE 10031, (2016).
• 22. Kvyetnyy R., Sofina O., Orlyk P., Utreras A., Wójcik W., et al., Improving the quality perception of digital images using modified method of the eye aberration correction, Proc. SPIE 10031, (2016).
• 23. Avrunin O., Pavlov S. Timchik S., Kisała P. et al., Classification of CT-brain slices based on local histograms, Proc. SPIE 9816, (2015).
• 24. Romanyuk O., Pavlov S., Melnyk O., Romanyuk S., Smolarz A., et al., Method of anti-aliasing with the use of the new pixel model, Proc. SPIE 9816, (2015).
• 25. Romanyuk S., Pavlov S., Melnyk O., New method to control color intensity for antialiasing, Control and Communications (SIBCON), 2015 International Siberian Conference, (2015).
• 26. Mashkov V., Smolarz A., Lytvynenko V., Gromaszek K., The problem of system fault-tolerance, Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Srodowiska, 4 (2014), 41-44.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).