Geodesic
Optimal estimation of a signal perturbed by a mixed fractional Brownian motion
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 62-68.

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We consider the problem of optimal estimation of the vector parameter $\theta$ of the drift term in a mixed fractional Brownian motion. We obtain the maximum likelihood estimator as well as the Bayesian estimator when the prior distribution is Gaussian.
Keywords: Mixed fractional Brownian motion; Maximum likelihood estimation; Bayes estimation. 
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B.L.S. Prakasa Rao. Optimal estimation of a signal perturbed by a mixed fractional Brownian motion. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 62-68. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a5/

[1] A. V. Artemov, E. V. Burnaev, “Optimal estimation of a signal perturbed by a fractional Brownian noise”, Theory Probab. Appl., 60 (2016), 126–134 | DOI | MR | Zbl

[2] C. Cai, P. Chigansky, M. Kleptsyna, “Mixed Gaussian processes”, Ann. Probab., 44 (2016), 3032–3075 | DOI | MR | Zbl

[3] P. Cheridito, “Mixed fractional Brownian motion”, Bernoulli, 7 (2001), 913–934 | DOI | MR | Zbl

[4] P. Chigansky, M. Kleptsyna, “Statistical analysis of the mixed fractional Ornstein-Uhlenbeck process”, arXiv: (2015). 1507.04194

[5] U. Cetin, A. Novikov, A. N. Shiryayev, “Bayesian sequential estimation of a drift of fractional Brownian motion”, Sequential Anal., 32 (2013), 288–296 | DOI | MR | Zbl

[6] Jose Luis da Silva, Mohamed Erraoui, El Hassan Essaky, “Mixed stochastic differential equations: Existence and uniqueness result”, arXiv: [math.PR] 1 Nov 2015. 1511.00191v1 | MR

[7] J. Guerra, D. Nualart, “Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion”, Stoch. Anal. Appl., 26 (2008), 1053–1075 | DOI | MR | Zbl

[8] Dmytro Marushkevych, “Large deviations for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process”, Modern Stochastics: Theory and Applications, 3 (2016), 107–117 | DOI | MR | Zbl

[9] Y. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, Lecture Notes in Mathematics, 1929, Springer, Berlin, 2008 | DOI | MR | Zbl

[10] Y. Mishura, G. Shevchenko, “Existence and uniqueness of the solution of stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H >1/2$”, Comm. Statist. Theory Methods, 40 (2011), 3492–3508 | DOI | MR | Zbl

[11] B. L. S. Prakasa Rao, “Parameter estimation for linear stochastic differential equations driven by fractional Brownian motion”, Random Oper. Stoch. Equ., 11 (2003), 229–242 | DOI | MR | Zbl

[12] B. L. S. Prakasa Rao, “Sequential estimation for fractional Ornstein-Uhlenbeck type process”, Sequential Anal., 23 (2004), 33–44 | DOI | MR | Zbl

[13] B. L. S. Prakasa Rao, “Sequential testing for simple hypotheses for processes driven by fractional Brownian motion”, Sequential Anal., 24 (2005), 189–203 | DOI | MR | Zbl

[14] B. L. S. Prakasa Rao, “Estimation for translation of a process driven by fractional Brownian motion”, Stoch. Anal. Appl., 23 (2005), 1199–1212 | DOI | MR | Zbl

[15] B. L. S. Prakasa Rao, “Estimation for stochastic differential equations driven by mixed fractional Brownian motions”, Calcutta Statistical Association Bulletin, 61 (2009), 143–153 | DOI | MR

[16] B. L. S. Prakasa Rao, Statistical Inference for Fractional Diffusion Processes, Wiley, London, 2010 | MR | Zbl

[17] B. L. S. Prakasa Rao, “Option pricing for processes driven by mixed fractional Brownian motion with superimposed jumps”, Probability in the Engineering and Information sciences, 29 (2015), 589–596 | DOI | MR | Zbl

[18] B. L. S. Prakasa Rao, “Pricing geometric Asian power options under mixed fractional Brownian motion environment”, Physica A, 446 (2015), 92–99 | DOI | MR

[19] B. L. S. Prakasa Rao, “Parameter estimation for linear stochastic differential equations driven by sub-fractional Brownian motion”, Random Oper. and Stoch. Equ., 25 (2017), 235–248 | MR

[20] B. L. S. Prakasa Rao, “Instrumental variable estimation for linear stochastic differential equations driven by mixed fractional Brownian motion”, Stoch. Anal. Appl., 35 (2017), 943–953 | DOI | MR | Zbl

[21] B. L. S. Prakasa Rao, “Optimal estimation of a signal perturbed by a sub-fractional Brownian motion”, Stoch. Anal. Appl., 35 (2017), 533–541 | DOI | MR | Zbl

[22] B. L. S. Prakasa Rao, “Parameter estimation for linear stochastic differential equations driven by mixed fractional Brownian motion Stoch. Anal. Appl.”, 2018 (to appear) | MR

[23] N. Rudomino-Dusyatska, “Properties of maximum likelihood estimates in diffusion and fractional Brownian models”, Theor. Probab. Math. Statist., 68 (2003), 139–146 | DOI | MR | Zbl

[24] G. Samarodnitsky, M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall, New York, 1994 | MR