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@article{THSP_2016_21_1_a8, author = {O. O. Synyavska}, title = {Interval estimation of the fractional {Brownian} motion parameter in a model with measurement error}, journal = {Teori\^a slu\v{c}ajnyh processov}, pages = {84--90}, publisher = {mathdoc}, volume = {21}, number = {1}, year = {2016}, language = {en}, url = {http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a8/} }
TY - JOUR AU - O. O. Synyavska TI - Interval estimation of the fractional Brownian motion parameter in a model with measurement error JO - Teoriâ slučajnyh processov PY - 2016 SP - 84 EP - 90 VL - 21 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a8/ LA - en ID - THSP_2016_21_1_a8 ER -
O. O. Synyavska. Interval estimation of the fractional Brownian motion parameter in a model with measurement error. Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 84-90. http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a8/
[1] T. Higuchi, “Approach to an irregular time series on the basis of fractal theory”, Physica D., 31 (1940), 277–283 | DOI | MR
[2] J.-M. Poggi, M.-C. Viano, “An estimate of the fractal index using multi-scale aggregates”, J. Time Series Anal., 19 (1998), 221–233 | DOI | MR | Zbl
[3] J.-F. Coeurjolly, “Estimating the parameters of a fractional Brownian motion by discrete variations of this sample paths”, Stat. Inference for Stoch. Process., 4 (2001), 199–207 | DOI | MR
[4] B. L. S. Prakasa Rao, Statistical Inference for Fractional Diffusion Processes, John Wiley Sons, Chichester, 2010 | MR | Zbl
[5] P. Levy, “Le mouvement Brownian plan”, Amer J. Math., 62 (1940), 487–550 | DOI | MR
[6] G. Baxter, “A strong limit theorem for Gaussian processes”, Proc. Amer. Math. Soc., 7:3 (1956), 522–527 | DOI | MR | Zbl
[7] J. M. Bardet, “Un test d'auto–similarite hour les processus gaussiences a accroissements stationares”, C. R. Acad. Sci. Paric., 328 (1999), 521–526 | DOI | MR | Zbl
[8] O. O. Kurchenko, “A strongly consistent estimate for the Hurst parameter of fractional Brownian motion”, Teor. Imovir. Mat. Stat., 67 (2002), 45–54 | MR
[9] J–C. Breton, I. Nourdin, G. Peccati, “Exact confidence intervals for the Hurst parameter of a fractional Brownian motion”, Electronic J. Statist., 3 (2009), 416–425 | DOI | MR | Zbl
[10] H. Schneeweiss, H. J. Mittag, Lineare Modelle mit fehlerbehafteten Daten, Physica-Verlag, Heidelberg, 1986 | MR
[11] R. J. Carroll, D. Ruppert, L. A. Stefanski, Measurement Error in Nonlinear Models, Chapman and Hall, London, 1995 | MR | Zbl
[12] C.–L. Cheng, J. W. Van Ness, Statistical Regression with Measurement Error, Arnold, London, 1999 | MR | Zbl
[13] A. Kukush, S. Shklyar, S. Masiuk, M. Chepurny, I. Likhtarov, Regression model with measurement errors and their application for estimation of radiation risk, Kyiv, 2015 (in Ukrainian)
[14] I. A. Ibragimov, Y. A. Rozanov, Gaussian random processes, Nauka, Moscow, 1970 (in Russian)
[15] G. M. Fikhtengolts, A Course of Differential and Integral Calculus, v. 1, Nauka, Moscow, 1969 (in Russian)