Results 21 to 30 of about 243,967 (218)
Fractal Stochastic Processes on Thin Cantor-Like Sets
Mathematics, 2021 We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh +1 more
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Axioms, 2022 We address here the space-fractional stochastic Hirota–Maccari system (SFSHMs) derived by the multiplicative Brownian motion in the Stratonovich sense. To acquire innovative elliptic, trigonometric and rational stochastic fractional solutions, we employ ...
Farah M. Al-Askar +3 more
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Approximations of fractional Brownian motion [PDF]
Bernoulli, 2011 Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process.
Li, Yuqiang, Dai, Hongshuai
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Complexity, 2021 In this article, we investigate a class of Caputo fractional stochastic differential equations driven by fractional Brownian motion with delays. Under some novel assumptions, the averaging principle of the system is obtained.
Pengju Duan, Hao Li, Jie Li, Pei Zhang
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Journal of Physics A: Mathematical and Theoretical, 2020 Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments.
Wei Wang +6 more
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Fuzzy stochastic differential equations driven by fractional Brownian motion
, 2021 In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence.
H. Jafari, M. T. Malinowski, M. J. Ebadi
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Dynamics of the Exponential Population Growth System with Mixed Fractional Brownian Motion
Complexity, 2021 This paper examines the dynamics of the exponential population growth system with mixed fractional Brownian motion. First, we establish some useful lemmas that provide powerful tools for studying the stochastic differential equations with mixed ...
Weijun Ma +3 more
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Neutral delay Hilfer fractional integrodifferential equations with fractional brownian motion
Evolution Equations and Control Theory, 2021 In this paper, we study the existence and uniqueness of mild solutions for neutral delay Hilfer fractional integrodifferential equations with fractional Brownian motion.
Yousef Alnafisah, H. Ahmed
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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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Averaging principles for mixed fast-slow systems driven by fractional Brownian motion [PDF]
Kyoto Journal of Mathematics, 2020 We focus on fast-slow systems involving both fractional Brownian motion (fBm) and standard Brownian motion (Bm). The integral with respect to Bm is the standard Ito integral, and the integral with respect to fBm is the generalised Riemann-Stieltjes ...
B. Pei, Y. Inahama, Yong Xu
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