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Parameter estimations for the sub-fractional Brownian motion with drift at discrete observation
Brazilian Journal of Probability and Statistics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuang, Nenghui, Liu, Bingquan
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The Lower Classes of the Sub-Fractional Brownian Motion
2011Let \(\{{B}_{H}(t),t \in{\mathbb{R}}^{\}}\) be a fractional Brownian motion with Hurst index 0 < H < 1. Consider the sub-fractional Brownian motion X H defined as follows : $${X}_{H}(t) = \dfrac{{B}_{H}(t) + {B}_{H}(-t)} {\sqrt{2}},t \geq0.$$ We characterize the lower classes of the sup-norm statistic of X H by an integral test.
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2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), 2017
A parametric identification problem for stochastic differential equation (SDE) with sub-fractional Brownian motion (sfBm) is considered in this paper. The task of parametric estimation is formulated as the constrained optimization problem, which is solved using a random search algorithm.
Dorota Bochnacka, Darya V. Filatova
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A parametric identification problem for stochastic differential equation (SDE) with sub-fractional Brownian motion (sfBm) is considered in this paper. The task of parametric estimation is formulated as the constrained optimization problem, which is solved using a random search algorithm.
Dorota Bochnacka, Darya V. Filatova
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More on maximal inequalities for sub-fractional Brownian motion
Stochastic Analysis and Applications, 2019AbstractWe derive some maximal inequalities for the sub-fractional Brownian motion using comparison theorems for Gaussian processes.
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Moduli of continuity of the local time of a class of sub-fractional Brownian motions
Random Operators and Stochastic Equations, 2017Abstract The aim of this paper is to establish sharp estimates for the moduli of continuity of the local time of a class of sub-fractional Brownian motions. We also investigate the continuity of their local times with respect to the self-similarity index.
Ait Ouahra, Mohamed, Guerbaz, Raby
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On some maximal and integral inequalities for sub-fractional Brownian motion
Stochastic Analysis and Applications, 2016ABSTRACTWe obtain a maximal inequality for sub-fractional Brownian motion with Hurst index analogous to the Burkholder–Davis–Gundy inequality for fractional Brownian motion derived by Novikov and Valkeila [Statist. Probab. Lett. 44(1999):47–54] and an integral inequality for Wiener integrals with respect to a sub-fractional Brownian motion with Hurst ...
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Journal of Mathematical Analysis and Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Communications in Statistics - Theory and Methods, 2015
ABSTRACTUsing multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of the adjusted quadratic variation for a sub-fractional Brownian motion. We apply our results to construct strongly consistent statistical estimators for the self-similarity of sub-fractional Brownian motion.
Junfeng Liu, Donglei Tang, Yuquan Cang
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ABSTRACTUsing multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of the adjusted quadratic variation for a sub-fractional Brownian motion. We apply our results to construct strongly consistent statistical estimators for the self-similarity of sub-fractional Brownian motion.
Junfeng Liu, Donglei Tang, Yuquan Cang
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Stochastic Analysis and Applications, 2017
ABSTRACTIn this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub ...
M. Ait Ouahra, A. Sghir
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ABSTRACTIn this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub ...
M. Ait Ouahra, A. Sghir
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Random Operators and Stochastic Equations
Abstract This paper is concerned with the existence of mild solutions for stochastic differential equations driven by mixed sub-fractional Brownian motion with Riemann–Liouville fractional derivative. The results are obtained by the fixed point theorem. An example is given to illustrate the obtained results.
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Abstract This paper is concerned with the existence of mild solutions for stochastic differential equations driven by mixed sub-fractional Brownian motion with Riemann–Liouville fractional derivative. The results are obtained by the fixed point theorem. An example is given to illustrate the obtained results.
Boutlilis, Mokhtaria +1 more
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