Results 21 to 30 of about 35,260 (265)
AIMS Mathematics, 2022 In this manuscript, we formulate the system of fuzzy stochastic fractional evolution equations (FSFEEs) driven by fractional Brownian motion. We find the results about the existence-uniqueness of the formulated system by using the Lipschitizian ...
Kinda Abuasbeh +3 more
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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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AIMS Mathematics, 2022 We consider the nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind defined by $ dX_t = \theta X_tdt+dY_t^{(1)}, t\geq 0, X_0 = 0 $ with an unknown parameter $ \theta > 0, $ where $ dY_t^{(1)} = e^{-t}dG_{a_{t}} $ and $ \{G_t, t\geq 0\}
Huantian Xie, Nenghui Kuang
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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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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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Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions [PDF]
, 2012 We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations that the optimal
Han, Yuecai, Hu, Yaozhong, Song, Jian
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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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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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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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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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