On bifractional Brownian motion
نویسندگان
چکیده
منابع مشابه
On the bifractional Brownian motion
This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of the fractional Brownian motion (which is obtained for K = 1). We adopt the strategy of the stochastic calculus via regularization. Particular inte...
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In this paper we introduce and study a self-similar Gaussian process that is the bifractional Brownian motion BH,K with parameters H ∈ (0, 1) and K ∈ (1, 2) such that HK ∈ (0, 1). A remarkable difference between the case K ∈ (0, 1) and our situation is that this process is a semimartingale when 2HK = 1.
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Let B = { B(t), t ∈ R+ } be a bifractional Brownian motion in R. We prove that B is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B , we establish Chung’s law of the iterated logarithm for B , as well as sharp Hölder conditions and tail probability estimates for the local times of B . We also consider the existence and the regularity of th...
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In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with absolutely continuous trajectories. Some applications of this decomposition are discussed.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2006
ISSN: 0304-4149
DOI: 10.1016/j.spa.2005.11.013