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Relevant bibliographies by topics / Fractional noise

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Academic literature on the topic 'Fractional noise'

Author: Grafiati

Published: 16 June 2022

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Journal articles on the topic "Fractional noise"

1

Wyss, Walter. "Fractional noise." Foundations of Physics Letters 4, no. 3 (June 1991): 235–46. http://dx.doi.org/10.1007/bf00665755.

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EL MELLALI, TARIK, and YOUSSEF OUKNINE. "WEAK CONVERGENCE FOR QUASILINEAR STOCHASTIC HEAT EQUATION DRIVEN BY A FRACTIONAL NOISE WITH HURST PARAMETER H ∈ (½, 1)." Stochastics and Dynamics 13, no. 03 (May 27, 2013): 1250024. http://dx.doi.org/10.1142/s0219493712500244.

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In this paper, we consider a quasi-linear stochastic heat equation in one dimension on [0, 1], with Dirichlet boundary conditions driven by an additive fractional white noise. We formally replace the random perturbation by a family of noisy inputs depending on a parameter n ∈ ℕ which can approximate the fractional noise in some sense. Then, we provide sufficient conditions ensuring that the real-valued mild solution of the SPDE perturbed by this family of noises converges in law, in the space [Formula: see text] of continuous functions, to the solution of the fractional noise driven SPDE.

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Sun, Xichao, and Junfeng Liu. "Weak Convergence for a Class of Stochastic Fractional Equations Driven by Fractional Noise." Advances in Mathematical Physics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/479873.

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We consider a class of stochastic fractional equations driven by fractional noise ont,x∈0,T×0,1 ∂u/∂t=Dδαu+ft,x,u+∂2BHt,x/∂t ∂x, with Dirichlet boundary conditions. We formally replace the random perturbation by a family of sequences based on Kac-Stroock processes in the plane, which approximate the fractional noise in some sense. Under some conditions, we show that the real-valued mild solution of the stochastic fractional heat equation perturbed by this family of noises converges in law, in the space𝒞0,T×0,1of continuous functions, to the solution of the stochastic fractional heat equation driven by fractional noise.

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Jin, Bangti, Yubin Yan, and Zhi Zhou. "Numerical approximation of stochastic time-fractional diffusion." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 4 (July 2019): 1245–68. http://dx.doi.org/10.1051/m2an/2019025.

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We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order α ∈ (0,1), and fractionally integrated Gaussian noise (with a Riemann-Liouville fractional integral of order γ ∈ [0,1] in the front). The numerical scheme approximates the model in space by the standard Galerkin method with continuous piecewise linear finite elements and in time by the classical Grünwald-Letnikov method (for both Caputo fractional derivative and Riemann-Liouville fractional integral), and the noise by the L2-projection. Sharp strong and weak convergence rates are established, using suitable nonsmooth data error estimates for the discrete solution operators for the deterministic inhomogeneous problem. One- and two-dimensional numerical results are presented to support the theoretical findings.

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Macias, Michal, Dominik Sierociuk, and Wiktor Malesza. "MEMS Accelerometer Noises Analysis Based on Triple Estimation Fractional Order Algorithm." Sensors 22, no. 2 (January 11, 2022): 527. http://dx.doi.org/10.3390/s22020527.

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This paper is devoted to identifying parameters of fractional order noises with application to noises obtained from MEMS accelerometer. The analysis and parameters estimation will be based on the Triple Estimation algorithm, which can simultaneously estimate state, fractional order, and parameter estimates. The capability of the Triple Estimation algorithm to fractional noises estimation will be confirmed by the sets of numerical analyses for fractional constant and variable order systems with Gaussian noise input signal. For experimental data analysis, the MEMS sensor SparkFun MPU9250 Inertial Measurement Unit (IMU) was used with data obtained from the accelerometer in x, y and z-axes. The experimental results clearly show the existence of fractional noise in this MEMS’ noise, which can be essential information in the design of filtering algorithms, for example, in inertial navigation.

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Safarinejadian, Behrouz, Nasrin Kianpour, and Mojtaba Asad. "State estimation in fractional-order systems with coloured measurement noise." Transactions of the Institute of Measurement and Control 40, no. 6 (March 15, 2017): 1819–35. http://dx.doi.org/10.1177/0142331217691219.

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This paper presents new estimation methods for discrete fractional-order state-space systems with coloured measurement noise. A novel approach is proposed to convert a fractional system with coloured measurement noise to a system with white measurement noise in which the process and measurement noises are correlated with each other. In this paper, two new Kalman filter algorithms for fractional-order linear state-space systems with coloured measurement noise, as well as a new extended Kalman filter algorithm for state estimation in nonlinear fractional-order state-space systems with coloured measurement noise, are proposed. The accuracy of the equations and relations is confirmed in several theorems. The validity and effectiveness of the proposed algorithms are verified by simulation results and compared with previous work. Results show that for linear and nonlinear fractional-order systems with coloured noise, the proposed methods are more accurate than conventional methods regarding estimation error and estimation error covariance. Simulation results demonstrate that the proposed algorithms can accurately perform estimation in fractional-order systems with coloured measurement noise.

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Lin, Lifeng, Huiqi Wang, Xipei Huang, and Yongxian Wen. "Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise." International Journal of Modern Physics B 32, no. 07 (March 5, 2018): 1850072. http://dx.doi.org/10.1142/s0217979218500728.

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For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro–Loginov formula and generalized fractional Shapiro–Loginov formula are derived. Then, by using the generalized (fractional) Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

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Li, Ming, Xichao Sun, and Xi Xiao. "Revisiting fractional Gaussian noise." Physica A: Statistical Mechanics and its Applications 514 (January 2019): 56–62. http://dx.doi.org/10.1016/j.physa.2018.09.008.

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Fa, Kwok Sau. "Fractional Ornstein–Uhlenbeck noise." Annals of Physics 393 (June 2018): 327–34. http://dx.doi.org/10.1016/j.aop.2018.04.019.

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Du, Wei, and Le Tong. "Introducing Robust Evolutionary Optimization in Noisy Fractional-Order Systems." International Journal of Bifurcation and Chaos 30, no. 08 (June 30, 2020): 2050119. http://dx.doi.org/10.1142/s0218127420501199.

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This paper investigates the problem of searching for the robust initial values of noisy fractional-order chaotic systems when the desired output is given. The problem is addressed under the framework of robust evolutionary optimization. Two different ways of adding noise are considered: (1) the noise is added to the initial point; (2) the noise is added to the orbit of the system. A series of experiments are conducted to validate the effectiveness of robust evolutionary optimization. The experimental results reveal that robust initial values of noisy fractional-order chaotic systems can be obtained in an efficient way by introducing robust evolutionary optimization.

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Dissertations / Theses on the topic "Fractional noise"

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Walkington, Robert. "New approaches in noise shaping fractional-N synthesis." Thesis, University College London (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406013.

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Moshrefi-Torbati, Mohamed. "Fractional calculus and its applications to dynamic systems." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296421.

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Kapfer, Maëlle. "Dynamic of excitations of the Fractional quantum Hall effect : fractional charge and fractional Josephson frequency." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS393/document.

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Dans certains états quantique de la matière, le courant peut être transporté par des porteurs de charges ayant une fraction e* de la charge élementaire. C'est notamment le cas de l'Effet Hall quantique fractionnaire (EHQF) qui se produit pour des systèmes électroniques bidimensionels à basse température et soumis à un fort champ magnetique perpendiculaire. Quand le nombre de quantum de flux en unité h/e est une fraction du nombre d'électrons, le courant se propage le long des bords de l'échantillon sans dissipation. Les porteurs de charges impliqués dans le transport portent une charge fractionnaire. La mise en évidence de ces charges peut être faite via les faibles fluctuations de courant dûes à la granularité de la charge. Nous présentons ici une méthode fiable de mesure de la charge fractionnaire basée sur des correlations croisées de fluctuations de courant. La dynamique de ces charges fractionnaires lorsque l'échantillon est irradié avec des photons GHz est étudiée, permettant la mesure de la fréquence Josephson des charges fractionnaires. Ces mesures valident les processus photo-assisté en régime d'EHQF et permettent une manipulation résolue en temps des charges fractionnaires, dans le but de réaliser une source d'anyon sur le principe du léviton afin de réaliser des tests de la statistique anyonique de ces charges fractionnaires
In some quantum matter states, the current may remarkably be transported by carriers that bear a fraction e* of the elementary electron charge. This is the case for the Fractional quantum Hall effect (FQHE) that happens in two-dimensional systems at low temperature under a high perpendicular magnetic field. When the number of magnetic flux in units of h/e is a fraction of the number of electron, a dissipationless current flows along the edges of the sample and is carried by anyons with fractional charge. The observation of the fractional charge is realized through small current fluctuations produced by the granularity of the charge. Here is presented a reliable method to measure the fractional charge by the mean of cross-correlation of current fluctuations. Moreover, the dynamical properties of those charges is probed when the sample is irradiated with photos at GHz frequency. The long predicted Josephson frequency of the fractional charge is measured. Those measurements validate Photoassisted processes in the FQHE and enable timedomain manipulation of fractional charges in order to realize a single anyon source based on levitons to perform tests of the anyonic statistics of fractional charge

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Giordano, Luca Maria. "Stochastic equations with fractional noise: continuity in law and applications." Doctoral thesis, Universitat Autònoma de Barcelona, 2020. http://hdl.handle.net/10803/670179.

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L’objectiu principal és estudiar la continuïtat en llei d’una família d’equacions diferencials parcials estocàstiques. Les equacions considerades són les equacions estocàstiques de calor i d’ones, en diversos ambients diferents. Suposem que el soroll sigui soroll blanc en la variable de temps i que sigui sorolls fraccionari, que depèn del paràmetre H, en la variable d’espai. Investiguem la dependència de les equacions del paràmetre H, demostrant que són contínues respecte a ell. També mostrem un resultat similar en el marc de la teoria de rough paths, en una configuració unidimensional. Finalment, donem una aplicació per a aquesta família de sorolls fraccionaris: modelem els preus de l’electricitat al mercat elèctric italià mitjançant un model impulsat per una equació fraccionaria.
El objetivo principal es estudiar la continuidad en la ley de una familia de ecuaciones diferenciales parciales estocásticas. Las ecuaciones consideradas son las ecuaciones estocásticas de calor y ondas, en varios entornos diferentes. Suponemos que el ruido sea ruido blanco en la variable de tiempo y que sea ruido fraccional, dependiendo del parámetro H, en la variable de espacio. Investigamos la dependencia de las ecuaciones del parámetro H, demostrando que son continuas con respecto a él. También mostramos un resultado similar en el marco de la teoría de rough paths, en un entorno unidimensional. En fin, damos una aplicación para esta familia de ruidos fraccionarios: modelamos los precios de la electricidad en el mercado liberalizado italiano de electricidad por medio de un modelo fraccionario.
The main objective is to study the continuity in law of a family of stochastic partial differential equations. The equations considered are the stochastic heat and wave equations, in various different settings. We suppose that the driving noise is white noise in the time variable and it is fractional noise, depending from the parameter H, in the space variable. We investigate the dependence of the equations from the parameter H, proving that they are continuous with respect to it. We also show a similar result in the framework of rough paths theory, in a one dimensional setting. Finally, we give an application for this family of fractional noises: we model the electricity prices in the liberalized Italian electricity market by means of a fractional-driven model.

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Neuenkirch, Andreas. "Optimal approximation of stochastic differential equations with additive fractional noise /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015005376&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Allegre, Daniel. "Reducing phase noise and spurious tones in fractional-n synthesizers." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1684.

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Jiang, D. "Design techniques for low-noise, high-speed fractional-N frequency synthesisers." Thesis, University College London (University of London), 2009. http://discovery.ucl.ac.uk/17932/.

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This thesis presents techniques for designing fractional-N synthesisers which achieve both low phase noise and high loop bandwidth simultaneously. The objective is to provide a single-loop synthesiser solution that satisfies the requirements on both the phase noise level and frequency switching speed specified by wireless standards. The GSM 900 standard is used as the bench- mark in this work but these techniques can also be applied to synthesisers for other wireless applications. A linearised synthesiser phase noise model is proposed for evaluating the proposed techniques. The model is constructed by characterising the major sources of synthesiser phase noise and integrating them with the loop transfer function. The accuracy of the model is validated by experimental results. As quantisation noise is one major source contributing to synthesiser phase noise, a number of novel noise reduction techniques are proposed. These techniques are based on \Sigma\Delta modulation and implemented with the stored-sequence method. A streamlined procedure for designing the \Sigma\Delta sequences is proposed. A prototype hardware synthesiser is developed with the proposed techniques. The synthesiser is designed for the GSM 900 standard with an output frequency range between 890 MHz and 960 MHz. The loop bandwidth is 250 kHz. Results obtained from measurements show that the synthesiser has a phase noise performance that meets GSM 900 phase noise specifications. Results also confirm the effectiveness of the proposed quantisation noise reduction technique. A new mechanism responsible for intermodulation effects in fractional-N synthesisers is described. It is found that fractional-N synthesisers are vulnerable to VCO-to-PFD coupling, which generates a family of spurious components in the synthesiser spectrum. Analytical and numerical models are developed to predict the magnitude and distribution of these spurs. The predictions are confirmed by results from hardware synthesiser experiments.

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Skeen, Matthew E. (Matthew Edward). "Maximum likelihood estimation of fractional Brownian motion and Markov noise parameters." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42527.

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Al-Talibi, Haidar. "On the Relevance of Fractional Gaussian Processes for Analysing Financial Markets." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1762.

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In recent years, the field of Fractional Brownian motion, Fractional Gaussian noise and long-range dependent processes has gained growing interest. Fractional Brownian motion is of great interest for example in telecommunications, hydrology and the generation of artificial landscapes. In fact, Fractional Brownian motion is a basic continuous process through which we show that it is neither a semimartingale nor a Markov process. In this work, we will focus on the path properties of Fractional Brownian motion and will try to check the absence of the property of a semimartingale. The concept of volatility will be dealt with in this work as a phenomenon in finance. Moreover, some statistical method like R/S analysis will be presented. By using these statistical tools we examine the volatility of shares and we demonstrate empirically that there are in fact shares which exhibit a fractal structure different from that of Brownian motion.

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Feng, Zijie. "Stock-Price Modeling by the Geometric Fractional Brownian Motion: A View towards the Chinese Financial Market." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-78375.

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As an extension of the geometric Brownian motion, a geometric fractional Brownian motion (GFBM) is considered as a stock-price model. The modeled GFBM is compared with empirical Chinese stock prices. Comparisons are performed by considering logarithmic-return densities, autocovariance functions, spectral densities and trajectories. Since logarithmic-return densities of GFBM stock prices are Gaussian and empirical stock logarithmic-returns typically are far from Gaussian, a GFBM model may not be the most suitable stock price model.

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Books on the topic "Fractional noise"

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Lütkemeyer, Christian. Konzeption eines Fractionally-Spaced Entzerrers mit quantisierter Rückkopplung und Noise-Whitening. Düsseldorf: VDI Verlag, 1999.

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Cheung, Yin-Wong. On maximum-likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean. Philadelphia: Federal Reserve Bank of Philadelphia, Economic Research Division, 1993.

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Aldridge, Irene. Can Humans Dance with Machines? Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190269999.003.0027.

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This chapter examines high-frequency trading (HFT), including core groups of strategies and resulting impacts. Using order-by-order market data analysis, the chapter shows that much of what is often construed to be useless noise of order cancellations actually represents meaningful order revisions, part of the real-time market bargaining. The chapter further shows that a small fraction of the order cancellations are a product of purely toxic liquidity. Market participants of different frequencies tend to react differently to such toxic orders, with higher-frequency traders largely ignoring and lower-frequency investors interacting with toxic liquidity.

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Book chapters on the topic "Fractional noise"

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Qian, Hong. "Fractional Brownian Motion and Fractional Gaussian Noise." In Processes with Long-Range Correlations, 22–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44832-2_2.

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Sheng, Hu, YangQuan Chen, and TianShuang Qiu. "Analysis of Biocorrosion Electrochemical Noise Using Fractional Order Signal Processing Techniques." In Fractional Processes and Fractional-Order Signal Processing, 189–202. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2233-3_9.

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Li, Ming. "Noise and Systems of Fractional Order." In Fractal Teletraffic Modeling and Delay Bounds in Computer Communications, 95–107. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003268802-5.

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Li, Ming. "Fractional Gaussian Noise and Traffic Modeling." In Fractal Teletraffic Modeling and Delay Bounds in Computer Communications, 109–26. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003268802-6.

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Li, Ming. "Generalized Fractional Gaussian Noise and Traffic Modeling." In Fractal Teletraffic Modeling and Delay Bounds in Computer Communications, 127–44. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003268802-7.

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Balan, Raluca M. "Recent Advances Related to SPDEs with Fractional Noise." In Seminar on Stochastic Analysis, Random Fields and Applications VII, 3–22. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0545-2_1.

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Chow, Winston C., and Edward J. Wegman. "Modeling Continuous Time Series Driven by Fractional Gaussian Noise." In Time Series Analysis and Applications to Geophysical Systems, 239–55. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4684-9386-3_13.

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Giraitis, L., and D. Surgailis. "On shot noise processes attracted to fractional Lévy motion." In Stable Processes and Related Topics, 261–73. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4684-6778-9_12.

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Sateesh, Vishnu Anugrahith, Iti Dutta, Rahul Priyadarshi, and Vijay Nath. "Fractional Frequency Reuse Scheme for Noise-Limited Cellular Networks." In Lecture Notes in Electrical Engineering, 995–1004. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5546-6_83.

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Chow, Winston C., and Edward J. Wegman. "Modeling Continuous Time Series Driven by Fractional Gaussian Noise." In Time Series Analysis and Applications to Geophysical Systems, 239–55. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4612-2962-9_13.

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Conference papers on the topic "Fractional noise"

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Manis, George, Matteo Bodini, Massimo W. Rivolta, and Roberto Sassi. "Bubble Entropy of Fractional Gaussian Noise and Fractional Brownian Motion." In 2021 Computing in Cardiology (CinC). IEEE, 2021. http://dx.doi.org/10.23919/cinc53138.2021.9662772.

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Crépieux, Adeline. "Photo-assisted shot noise in the fractional quantum Hall regime." In NOISE AND FLUCTUATIONS: 18th International Conference on Noise and Fluctuations - ICNF 2005. AIP, 2005. http://dx.doi.org/10.1063/1.2036799.

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Vivero, Oskar, and William P. Heath. "Regularised estimators for fractional Gaussian noise." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717764.

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Dolcini, Fabrizio. "Current Noise in Non-Chiral Luttinger Liquids: Appearance of Fractional Charge." In NOISE AND FLUCTUATIONS: 18th International Conference on Noise and Fluctuations - ICNF 2005. AIP, 2005. http://dx.doi.org/10.1063/1.2036783.

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Meade, M. L. "Discrete-time fGn and fBm obtained by fractional summation." In Noise in physical systems and 1/. AIP, 1993. http://dx.doi.org/10.1063/1.44623.

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Saichev, Alexander I., and Sergei G. Utkin. "Random walks models with intermediate fractional diffusion asymptotics." In Second International Symposium on Fluctuations and Noise, edited by Zoltan Gingl. SPIE, 2004. http://dx.doi.org/10.1117/12.546833.

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Akhtar, Muhammad Tahir, and Muhammad AsifZahoor Raja. "Fractional processing-based active noise control algorithm for impulsive noise." In 2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP). IEEE, 2015. http://dx.doi.org/10.1109/chinasip.2015.7230352.

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Ortigueira, Manuel Duarte, and Arnaldo Guimara˜es Batista. "A New Look at the Fractional Brownian Motion Definition." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35218.

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A reinterpretation of the classic definition of fractional Brownian motion leads to a new definition involving a fractional noise obtained as a fractional derivative of white noise. To obtain this fractional noise, two sets of fractional derivatives are considered: a) the forward and backward and b) the central derivatives. For these derivatives the autocorrelation functions of the corresponding fractional noises have the same representations. The obtained results are used to define and propose a new simulation procedure.

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Nualart, David. "A white noise approach to fractional Brownian motion." In Stochastic Analysis: Classical and Quantum - Perspectives of White Noise Theory. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701541_0010.

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Paola, Mario Di, Giuseppe Failla, and Antonina Pirrotta. "Fractional Viscoelastic Systems under Normal White Noise." In 6th International Conference on Computational Stochastic Mechanics. Singapore: Research Publishing Services, 2011. http://dx.doi.org/10.3850/978-981-08-7619-7_p023.

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Reports on the topic "Fractional noise"

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Chow, Winston C. Estimation Theory with Fractional Gaussian Noise. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada301443.

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Tan, Cheng-Yang. A boostrap algorithm for temporal signal reconstruction in the presence of noise from its fractional Fourier transformed intensity spectra. Office of Scientific and Technical Information (OSTI), February 2011. http://dx.doi.org/10.2172/1009591.

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Dolan, Daniel H. Limiting noise fraction in PDV measurements. Office of Scientific and Technical Information (OSTI), October 2018. http://dx.doi.org/10.2172/1481558.

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