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A Journal of Theoretical and Applied Statistics
Volume 49, 2015 - Issue 1
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Original Articles

On drift parameter estimation in models with fractional Brownian motion

Y. KozachenkoDepartment of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska, 60, 01601Kyiv, Ukraine
,
A. MelnikovDepartment of Mathematical and Statistical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, AB, CanadaT6G 2G1Correspondence[email protected]
&
Y. MishuraDepartment of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics Faculty, Taras Shevchenko National University of Kyiv, Volodymyrska, 60, 01601Kyiv, Ukraine
Pages 35-62 | Received 15 Sep 2011, Accepted 14 Mar 2014, Published online: 23 Apr 2014

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Alexander Melnikov & Andrey Pak. (2023) Parameter estimation in optional semimartingale regression models. Statistics 57:5, pages 1165-1201.
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Yuliya Mishura, Kostiantyn Ralchenko & Hanna Zhelezniak. (2022) Numerical approach to the drift parameter estimation in the model with two fractional Brownian motions. Communications in Statistics - Simulation and Computation 0:0, pages 1-15.
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Articles from other publishers (32)

Yuliya Mishura & Kostiantyn Ralchenko. (2024) Fractional diffusion Bessel processes with Hurst index . Statistics & Probability Letters 206, pages 110008.
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Yuliya Mishura & Kostiantyn Ralchenko. (2024) Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models. Fractal and Fractional 8:2, pages 79.
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Yuliya Mishura & Anton Yurchenko-Tytarenko. (2023) Parameter Estimation in Rough Bessel Model. Fractal and Fractional 7:7, pages 508.
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Shohei Nakajima & Yasutaka Shimizu. (2022) Asymptotic inference for stochastic differential equations driven by fractional Brownian motion. Japanese Journal of Statistics and Data Science 6:1, pages 431-455.
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Diana Avetisian & Kostiantyn Ralchenko. (2023) Parameter estimation in mixed fractional stochastic heat equation. Modern Stochastics: Theory and Applications, pages 175-195.
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Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen, Soledad Torres & Ciprian Tudor. (2021) Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation. Scandinavian Journal of Statistics 49:3, pages 992-1022.
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Paul Hager & Eyal Neuman. (2022) The multiplicative chaos of H=0 fractional Brownian fields. The Annals of Applied Probability 32:3.
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Yuliya Mishura & Nakahiro Yoshidae. (2022) Divergence of an integral of a process with small ball estimate. Stochastic Processes and their Applications 148, pages 1-24.
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Alexander Kukush, Stanislav Lohvinenko, Yuliya Mishura & Kostiantyn Ralchenko. (2021) Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend. Statistical Inference for Stochastic Processes 25:1, pages 159-187.
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Chun-Hao Cai, Yin-Zhong Huang, Lin Sun & Wei-Lin Xiao. (2022) Maximum Likelihood Estimation for Mixed Fractional Vasicek Processes. Fractal and Fractional 6:1, pages 44.
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Olha Hopkalo & Lyudmyla Sakhno. (2021) Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes. Modern Stochastics: Theory and Applications, pages 41-62.
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STOYAN V. STOYANOV, SVETLOZAR T. RACHEV, STEFAN MITTNIK & FRANK J. FABOZZI. (2019) PRICING DERIVATIVES IN HERMITE MARKETS. International Journal of Theoretical and Applied Finance 22:06, pages 1950031.
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Yanghui Liu, Eulalia Nualart & Samy Tindel. (2019) LAN property for stochastic differential equations with additive fractional noise and continuous time observation. Stochastic Processes and their Applications 129:8, pages 2880-2902.
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Hui Jiang, Junfeng Liu & Shaochen Wang. (2019) Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process. Stochastics and Dynamics 19:03, pages 1950018.
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Stanislav Lohvinenko & Kostiantyn Ralchenko. (2019) Maximum likelihood estimation in the non-ergodic fractional Vasicek model. Modern Stochastics: Theory and Applications, pages 377-395.
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Weilin Xiao, Xili Zhang & Ying Zuo. (2018) Least squares estimation for the drift parameters in the sub-fractional Vasicek processes. Journal of Statistical Planning and Inference 197, pages 141-155.
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Samudrajit Thapa, Michael A. Lomholt, Jens Krog, Andrey G. Cherstvy & Ralf Metzler. (2018) Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data. Physical Chemistry Chemical Physics 20:46, pages 29018-29037.
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Tommi Sottinen & Lauri Viitasaari. (2017) Parameter estimation for the Langevin equation with stationary-increment Gaussian noise. Statistical Inference for Stochastic Processes 21:3, pages 569-601.
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Jens Krog, Lars H Jacobsen, Frederik W Lund, Daniel Wüstner & Michael A Lomholt. (2018) Bayesian model selection with fractional Brownian motion. Journal of Statistical Mechanics: Theory and Experiment 2018:9, pages 093501.
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Marco Dozzi, Yuriy Kozachenko, Yuliya Mishura & Kostiantyn Ralchenko. (2016) Asymptotic growth of trajectories of multifractional Brownian motion, with statistical applications to drift parameter estimation. Statistical Inference for Stochastic Processes 21:1, pages 21-52.
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. 2018. Stochastic Analysis of Mixed Fractional Gaussian Processes. Stochastic Analysis of Mixed Fractional Gaussian Processes 185 192 .
Yuliya Mishura, Kostiantyn Ralchenko & Sergiy Shklyar. 2018. Stochastic Processes and Applications. Stochastic Processes and Applications 123 146 .
Alexander Kukush, Yuliya Mishura & Kostiantyn Ralchenko. (2017) Hypothesis testing of the drift parameter sign for fractional Ornstein–Uhlenbeck process. Electronic Journal of Statistics 11:1.
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Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 269 320 .
Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 161 267 .
Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 125 160 .
Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 75 123 .
Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 45 74 .
Kęstutis Kubilius, Yuliya Mishura & Kostiantyn RalchenkoKęstutis Kubilius, Yuliya Mishura & Kostiantyn Ralchenko. 2017. Parameter Estimation in Fractional Diffusion Models. Parameter Estimation in Fractional Diffusion Models 1 43 .
Yuliya Mishura & Kostiantyn Ralchenko. 2017. Modern Problems of Stochastic Analysis and Statistics. Modern Problems of Stochastic Analysis and Statistics 237 268 .
Kęstutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko & Oleg Seleznjev. (2015) Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index $H\in(0,\frac{1}{2})$. Electronic Journal of Statistics 9:2.
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Enkelejd Hashorva & Lanpeng Ji. (2018) Approximation of Passage Times of γ-Reflected Processes with FBM Input. Journal of Applied Probability 51:3, pages 713-726.
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