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On Squared Fractional Brownian Motions [PDF]
, 2004 We have proved recently that fractional Brownian motions with Hurst parameter H in (0, 1/2) satisfy a remarkable property: their squares are infinitely divisible. In the Brownian motion case (the case H = 1/2), this property is completely understood thanks to stochastic calculus arguments.
Eisenbaum, N., Tudor, C.A.
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Fractal and Fractional, 2022 As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention.
Hongwen Hu +3 more
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The fractional mixed fractional brownian motion and fractional brownian sheet [PDF]
ESAIM: Probability and Statistics, 2007 Summary: We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test.
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Prediction law of fractional Brownian motion [PDF]
Statistics & Probability Letters, 2017 We calculate the regular conditional future law of the fractional Brownian motion with index $H\in(0,1)$ conditioned on its past. We show that the conditional law is continuous with respect to the conditioning path. We investigate the path properties of the conditional process and the asymptotic behavior of the conditional covariance.
Viitasaari, Lauri, Sottinen, Tommi
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Anticipated BSDEs Driven by Fractional Brownian Motion with a Time-Delayed Generator
Mathematics, 2023 This article describes a new form of an anticipated backward stochastic differential equation (BSDE) with a time-delayed generator driven by fractional Brownian motion, further known as fractional BSDE, with a Hurst parameter H∈(1/2,1).
Pei Zhang +2 more
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Search efficiency of discrete fractional Brownian motion in a random distribution of targets
Physical Review Research, 2021 Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of Lévy walks, a specific range of optimal efficiencies was suggested under variation of search intrinsic and ...
S. Mohsen J. Khadem +2 more
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Operator Fractional Brownian Motion and Martingale Differences
Abstract and Applied Analysis, 2014 It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both
Hongshuai Dai +2 more
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Asset Pricing Model Based on Fractional Brownian Motion
Fractal and Fractional, 2022 This paper introduces one unique price motion process with fractional Brownian motion. We introduce the imaginary number into the agent’s subjective probability for the reason of convergence; further, the result similar to Ito Lemma is proved.
Yu Yan, Yiming Wang
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Mixed Fractional Brownian Motion [PDF]
Bernoulli, 2001 Let \(B\) be the standard Brownian motion and \(B^H\) fractional Brownian motion with Hurst index \(H\in (0,1]\). If the Brownian motion \(B\) and the fractional Brownian motion \(B^H\) are independent and \(\alpha\in\mathbb{R} \setminus \{0\}\), define the mixed fractional Brownian motion \(M^{H,\alpha}\) by \(M^{H,\alpha} \doteq B+\alpha B^H\).
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重分数布朗运动的列维连续模(Lévy's moduli of continuity of multifractional Brownian motion)
Zhejiang Daxue xuebao. Lixue ban, 2000 This paper proposed Lévy's moduli of continuity of multifractional Brownian motion,which is a generalization of the fractional Brownian motion.
LINZheng-yan(林正炎)
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