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Keywords
(5)
bifractional brownian motion
Chaos Expansion
Stochastic Integral
Tail Probability
Local Time
Related Publications
(4)
On bifractional Brownian motion
Quadratic Variations along Irregular Subdivisions for Gaussian Processes
Multidimensional bifractional Brownian motion: Ito and Tanaka formulas
SPHERICAL AND HYPERBOLIC FRACTIONAL BROWNIAN MOTION
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Sample Path Properties of Bifractional Brownian Motion
Sample Path Properties of Bifractional Brownian Motion,Ciprian A. Tudor,Yimin Xiao
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Sample Path Properties of Bifractional Brownian Motion
(
Citations: 14
)
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Ciprian A. Tudor
,
Yimin Xiao
Let $B^{H, K}= \big\{B^{H, K}(t), t \in \R_+ \big\}$ be a
bifractional Brownian motion
in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a
stochastic integral
representation of $B^{H, K}$, we establish Chung's law of the iterated logarithm for $B^{H, K}$, as well as sharp H\"older conditions and
tail probability
estimates for the local times of $B^{H, K}$. We also consider the existence and the regularity of the local times of multiparameter
bifractional Brownian motion
$B^{\bar{H}, \bar{K}}= \big\{B^{\bar{H}, \bar{K}}(t), t \in \R^N_+ \big\}$ in $\R^d$ using WienerIt\^o chaos expansion.
Published in 2006.
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Citation Context
(6)
...A stochastic analysis for this process can be found in [
7
] and a study of its occupation density has been done in [
2
] and [
14
]...
Khalifa EsSebaiy
,
et al.
Occupation densities for certain processes related to fractional Brown...
...so relation (2.5) holds with � = HK. A stochastic analysis for this process can be found in [7] and a study of its occupation densities has been done in [2], [
12
]...
Khalifa EsSebaiy
,
et al.
Occupation densities for certain processes related to fractional Brown...
...Introduced in [4], the bifractional Brownian motion, a generalization of the fractional Brownian motion, has been studied in many aspects (see [1], [3], [6], [7], [8], [9] and [
10
])...
Makoto Maejima
,
et al.
Limits of bifractional Brownian noises
...The process bfBm is also studied in [14,
19
]...
Tomasz Bojdecki
,
et al.
Some extensions of fractional Brownian motion and subfractional Brown...
...Other papers treated different aspects of this stochastic process, like sample pats properties, extension of the parameters or statistical applications (see [6], [4], [
22
] or [11]...
...We start with the one dimensional bifBm and we first derive an Itˆo and an Tanaka formula for it when 2HK ≥ 1. We mention that the Itˆo formula has been already proved by [
15
] but here we propose an alternative proof based on the Taylor expansion which appears to be also useful in the multidimensional settings...
...It follows actually from [
15
] that the space H is a Banach space for the norm k � k H and it is included in H. In fact,...
...This paragraph is consecrated to the proof of Itˆo formula and Tanaka formula for the onedimensional bifractional Brownian motion with 2HK ≥ 1. Note that the Itˆo formula has been already proved in [
15
]; here we propose a different approach based on the Taylor expansion which be also used in the multidimensional settings...
...This term (in fact, slightly modified) appeared in some other papers such as Proposition 12 in [10], or in [
22
]...
Ciprian Tudor
,
et al.
Multidimensional bifractional Brownian motion: Ito and Tanaka formulas
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Citations
(14)
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Occupation densities for certain processes related to fractional Brownian motion
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