On some local asymptotic properties of sequences with a random index
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https://doi.org/10.21638/spbu01.2020.308Abstract
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Литература
1. Мандельброт Б. Фракталы, случай и финансы. М.: РХД, 2004.
2. Мандельброт Б., Хадсон Р.Л. (Не)послушные рынки. Фрактальная революция в финансах. М.: Вильямс, 2006.
3. Wolpert R. L., Taqqu M. S. Fractional Ornstein-Uhlenbeck L´evy Processes and the Telecom Process: Upstairs and Downstairs // Signal Processing. 2005. Vol. 85. Iss. 8. P. 1523–1545. https://doi.org/10.1016/j.sigpro.2004.09.016
4. Reif F. Fundamentals of Statistical and Thermal Physics. New York: McGraw Hill, 1965.
5. Lamperti J.W. Semi-stable Stochastic Processes // Trans. Amer. Math. Soc. 1962. Vol. 104. P. 62–78.
6. Barndorff-Nielsen O.E., P´erez-Abreu V. Stationary and Self-similar Processes Driven by L´evy Processes // Stochastic Processes and their Applications. 1999. Vol. 84. Iss. 2. P. 357-369. https://doi.org/10.1016/S0304-4149(99)00061-7
7. Rusakov O., Laskin M. Self-Similarity in the Wide Sense for Information Flows with a Random Load Free on Distribution // 2017 European Conference on Electrical Engineering and Computer Science (EECS), Bern, Switzerland, 2018. P. 142–146. https://doi.org/10.1109/EECS.2017.35
8. Hu Y., Nualart D., Zhou H. Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter // Statistical Inference for Stochastic Processes. 2017. Vol. 22. Iss. 1. P. 111–142.
9. Русаков О.В. Относительная компактность сумм независимых одинаково распределенных псевдопуассоновских процессов в пространстве Скорохода // Зап. научн. сем. ПОМИ. 2015. Т. 442. C. 122–132.
10. Kac M. A stochastic model related to the telegrapher’s equation // Rocky Mountain. J. Math. 1974. Vol. 4. P. 497–510. https://doi.org/10.1216/RMJ-1974-4-3-497
11. Кингман Дж. Пуассоновские процессы. М.: Изд-во МЦНМО, 2007.
12. Русаков О.В. Псевдо-пуассоновские процессы со стохастической интенсивностью и класс процессов, обобщающих процесс Орнштейна-Уленбека // Вестн. С.-Петерб. ун-та. Математика. Механика. Астрономия. 2017. Т. 4(62). Вып. 2. С. 247–257. https://doi.org/10.21638/11701/spbu01.2017.208
13. Дуб Дж.Л. Вероятностные процессы. М.: Изд-во иностр. лит., 1956.
14. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.
15. Parthasarathy K.R., Varadhan S.R.S. Extension of Stationary Stochastic Processes // Теория вероятн. и ее примен. 1964. Т. 9. Вып. 1. С. 72–78.
References
1. Mandelbrot B., Fractales, Hasard Et Finance (Flammarion, Paris, 2009).
2. Mandelbrot B., Hudson R. L., The (mis)behavior of markets. A fractal view of risk, ruin, and reward (Basic Books, New York, 2006).
3. Wolpert R. L., Taqqu M. S., “Fractional Ornstein-Uhlenbeck L´evy Processes and the Telecom process: upstairs and downstairs”, Signal Processing 85(8), 1523–1545 (2005). https://doi.org/10.1016/j.sigpro.2004.09.016
4. Reif F., Fundamentals of statistical and thermal physics (McGraw-Hill, New York, 1965).
5. Lamperti J.W., “Semi-stable stochastic processes”, Trans. Amer. Math. Soc. 104, 62–78 (1962).
6. Barndorff-Nielsen O.E., P´erez-Abreu V., “Stationary and self-similar processes driven by L´evy processes”, Stoch. Proc. Appl. 84(2), 357–369 (1999). https://doi.org/10.1016/S0304-4149(99)00061-7
7. Rusakov O., Laskin M., “Self-similarity in the wide sense for information flows with a random load free on distribution”, in 2017 European Conference on Electrical Engineering and Computer Science (EECS), Bern, Switzerland, 142–146 (2018). https://doi.org/10.1109/eecs.2017.35
8. Hu Y., Nualart D., Zhou H., “Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter”, Stat. Inference Stoch. Process. 22(1), 111–142 (2017).
9. Rusakov O.V., “Tightness of the sums of independent identically distributed pseudo-poissonian processes in the Skorokhod space”, J. Math. Sci. 225, 805–811 (2017). https://doi.org/10.1007/s10958-017-3496-z
10. Kac M., “A stochastic model related to the telegrapher’s equation” Rocky Mountain. J. Math. 4, 497–510 (1974). https://doi.org/10.1216/RMJ-1974-4-3-497
11. Kingman J.F.C., Poisson processes (Claderon Press, Oxford, 1993).
12. Rusakov O.V., “Pseudo-Poisson processes with stochastic intensity and a class of processes which generalize the Ornstein-Uhlenbeck process”, Vestnik St. Petersburg University: Mathematics. 50, 153–160 (2017). https://doi.org/10.3103/S106345411702011X
13. Doob J. L., Stochastic processes (John Wiley and Sons, New York, 1953).
14. Abramowitz M., Stegun I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972).
15. Parthasarathy K.R., Varadhan S.R. S., “Extension of Stationary Stochastic Processes”, Theory Probab. Appl. 9(1), 65–71 (1964). https://doi.org/10.1137/1109006
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Published
2020-09-04
How to Cite
Rusakov, O. V., Baev, B. A., & Yakubovich, Y. V. (2020). On some local asymptotic properties of sequences with a random index. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(3), 453–468. https://doi.org/10.21638/spbu01.2020.308
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Mathematics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
