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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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Fractional Brownian Motions [PDF]
Acta Physica Polonica B, 2020 Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ.
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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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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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Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion [PDF]
Theory of Probability & Its Applications, 2022 Рассматривается вероятность персистентности для интегрированного дробного броуновского движения и дробно интегрированного броуновского движения с параметром $H$. Для интегрированного дробного броуновского движения обсуждается гипотеза Молчана- Хохлова и устанавливается асимптотическое поведение показателя персистентности при $H\to0$ и при $H\to1 ...
Aurzada, F., Kilian, M.
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Oscillatory Fractional Brownian Motion [PDF]
Acta Applicandae Mathematicae, 2013 The authors ``introduce oscillatory analogues of fractional Brownian motion [(fBm)], subfractional Brownian motion [(sfBm)] and other related long range dependent Gaussian processes.'' According to them, the oscillatory fractional Brownian motion (ofBm) is a centered Gaussian process \(\xi ^{H}\), with parameter \(H\in (1/2,1)\) and covariance function
Bojdecki, T. +2 more
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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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ReLink: Reliable Deep Learning for Microscopic Motion Tracking. [PDF]
Adv Sci (Weinh)ReLink enables reliable trajectory linking in single‐particle tracking by integrating physics‐informed motion statistics with confidence‐based adaptive filtering. Across diverse simulated and experimental conditions, ReLink robustly reconstructs trajectories and preserves the fidelity of downstream analyses, enabling accurate characterization of ...
Jiang Y +7 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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