Acceso abierto

Nonparametric estimation of trend function for stochastic differential equations driven by a bifractional Brownian motion


Cite

[1] X. Bardina, K. Es-Sebaiy, An extension of bifractional Brownian motion, Communications on Stochastic Analysis, 5 (2) (2011), 333–340.10.31390/cosa.5.2.05Search in Google Scholar

[2] K. Es-Sebaiy and C. A. Tudor, Multidimensional bifractional Brownian motion: Itô and Tanaka formulas, Stoch. Dyn., 7 (3) (2007), 365–388.10.1142/S0219493707002050Search in Google Scholar

[3] C. Houdré and J. Villa, An example of infinite dimensional quasi-helix, Stochastic models (Mexico City, 2002), Contemp. Math., 336 (2003), 195–201.10.1090/conm/336/06034Search in Google Scholar

[4] J. P. Kahane, Hélices et quasi-hélices, Adv. Math., 7B (1981), 417–433.Search in Google Scholar

[5] A. N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C.R. (Doklady) Acad. USSR (N.S.), 26 (1940), 115–118.Search in Google Scholar

[6] I. Kruk, F. Russo, and C. A. Tudor, Wiener integrals, Malliavin calculus and covariance measure structure, J. Funct. Anal., 249 (1) (2007), 92–142.10.1016/j.jfa.2007.03.031Search in Google Scholar

[7] Y. A. Kutoyants, Identification of dynamical systems with small noise, Springer Science & Business Media, 300 (2012).Search in Google Scholar

[8] M. Lifshits, K. Volkova, Bifractional Brownian motion: Existence and Border cases, preprint. http://arxiv.org/pdf/1502.02217.pdf., (2015).Search in Google Scholar

[9] B. B. Mandelbrot, J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10 (1968), 422–437.10.1137/1010093Search in Google Scholar

[10] M. N. Mishra and B. L. S. Prakasa Rao, Nonparameteric Estimation of Trend for Stochastic Differential Equations Driven by Fractional Brownian Motion, Stat. Inference. Stoch. Process., 14 (2011), 101–109.10.1007/s11203-010-9051-xSearch in Google Scholar

[11] M. N. Mishra, B. L. S. Prakasa Rao, Nonparametric Estimation of Linear Multiplier for Fractional Diffusion processes, Stochastic Analysis and Application, 29 (2011), 706–712.10.1080/07362994.2011.581109Search in Google Scholar

[12] I. Norros, E. Valkeila, J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli, 5 (4) (1999), 571–587.10.2307/3318691Search in Google Scholar

[13] B. L. S. Prakasa Rao, Nonparametric estimation of trend for stochastic differential equations driven by mixed fractional Brownian motion, Stochastic Analysis and Applications, 37 (2) (2019), 271–280.10.1080/07362994.2018.1555045Search in Google Scholar

[14] F. Russo and C. Tudor, On the bifractional Brownian motion, Stoch. Process. Their Appl., 116 (5) (2006), 830–856.10.1016/j.spa.2005.11.013Search in Google Scholar

[15] B. Saussereau, Nonparametric inference for fractional diffusion, Bernoulli, 20 (2) (2014), 878–918.10.3150/13-BEJ509Search in Google Scholar

[16] C. A. Tudor, Y. Xiao, Sample path properties of bifractional Brownian motion, Bernoulli13 (2007), 1023–1052.10.3150/07-BEJ6110Search in Google Scholar

[17] L. Yan, J. Liu, and G. Jing, Quadratic covariation and Itôformula fora bifractional Brownian motion, preprint (2008).Search in Google Scholar

eISSN:
2066-7752
Idioma:
Inglés
Calendario de la edición:
2 veces al año
Temas de la revista:
Mathematics, General Mathematics