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Sub-fractional Brownian motion and its relation to occupation times [PDF]

Statistics & Probability Letters, 2004
The authors study a class of centered Gaussian processes on \([0,\infty)\) which they call ``sub-fractional Brownian motions''. The covariance function is given by \[ s^h + t^h -\tfrac{1}{2}\left[ (s+t)^h +| s-t| ^h\right]\;,\quad t,s\geq 0\;, \] for a certain \(h\in (0,2)\). Of course, if \(h=1\), one gets the ordinary Brownian motion.
Tomasz Bojdecki, Luis G. Gorostiza, Anna Talarczyk   +2 more
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Optimal estimation of a signal perturbed by a sub-fractional Brownian motion

Stochastic Analysis and Applications, 2017
ABSTRACTWe consider the problem of optimal estimation of the vector parameter θ of the drift term in a sub-fractional Brownian motion. We obtain the maximum likelihood estimator as well as Bayesian estimator when the prior distribution is Gaussian.
B L S Prakasa Rao
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On the collision local time of sub-fractional Brownian motions

Statistics & Probability Letters, 2010
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Yan, Litan, Shen, Guangjun
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Strong Local Non-Determinism of Sub-Fractional Brownian Motion

Applied Mathematics, 2015
Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.
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Asymptotic behavior of weighted cubic variation of sub-fractional brownian motion

Communications in Statistics - Simulation and Computation, 2014
ABSTRACTIn this article, we investigate the convergence of renormalized weighted cubic variation of a sub-fractional Brownian motion SH with Hurst index H. When , we prove by means of Malliavin calculus that the convergence holds in L2 toward an explicit limit which only depends on SH. We also numerically simulate the sample paths of such a type of sub-
Nenghui Kuang, Huantian Xie
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The increments of a sub-fractional Brownian motion

2016 International Conference on Information and Digital Technologies (IDT), 2016
The sub-fractional Brownian motion {X H (t), t ≥ 0} with Hurst index 0 H consists mainly in investigating their limit properties under suitable conditions. The lim sup behavior was already investigated. It depends on two constants : the first one occurs in the quasi-helix property whereas the second one in the approximately stationary increments ...
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Fuzzy simulation of European option pricing using sub-fractional Brownian motion

Chaos, Solitons & Fractals, 2021
Abstract On the basis of the sub-fractional Black-Scholes model, considering that the financial market is uncertain with randomness and fuzziness, we used stochastic analysis, fractal theory and fuzzy set theory to construct European option pricing model based on the long-term memory property of the financial market in an uncertain environment ...
Liu Bian, Zhi Li
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Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk

Annals of the Institute of Statistical Mathematics, 2013
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Huantian Xie
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Remarks on an integral functional driven by sub-fractional Brownian motion

Journal of the Korean Statistical Society, 2011
This paper studies the functionals \[ A_{1}(t,x)=\int_{0}^{t}1_{\left[ 0,\infty \right) }\left( x-S_{s}^{H}\right) ds, \] \[ A_{2}(t,x)=\int_{0}^{t}1_{\left[ 0,\infty \right) }\left( x-S_{s}^{H}\right) s^{2H-1}ds, \] where \(\left( S_{s}^{H}\right) _{0\leq s\leq T}\) is a one-dimension sub-fractional Brownian motion with index \(H\in (0,1)\).
Shen, Guangjun, Yan, Litan
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An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion

Stochastics and Dynamics, 2023
In this paper, we introduce fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (SFBM) which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The SFBM is an extension of the Brownian motion that retains many properties of fractional Brownian motion (FBM), but not the ...
Jafari, Hossein, Farahani, Hamed
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