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Journal articles on the topic 'White noise'

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Published: 4 June 2021
Last updated: 30 July 2024

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1

Tellis, Ashley. "White Noise." Transforming Anthropology 13, no. 2 (October 2005): 148–49. http://dx.doi.org/10.1525/tran.2005.13.2.148.

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2

George David Clark. "WHITE NOISE." Antioch Review 72, no. 1 (2014): 149. http://dx.doi.org/10.7723/antiochreview.72.1.0149.

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3

Lööw, Heléne. "White Noise." Index on Censorship 27, no. 6 (November 1998): 153–55. http://dx.doi.org/10.1080/03064229808536482.

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4

morton, mark. "White Noise." Gastronomica 9, no. 3 (2009): 6–7. http://dx.doi.org/10.1525/gfc.2009.9.3.6.

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5

Banerjee, Mousumi. "White Noise." JAMA Oncology 4, no. 12 (December 1, 2018): 1793. http://dx.doi.org/10.1001/jamaoncol.2018.4644.

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6

Nobes, Karen, and Susan Kerrigan. "White noise." Alphaville: Journal of Film and Screen Media, no. 24 (December 20, 2022): 79–96. http://dx.doi.org/10.33178/alpha.24.05.

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First Nations content on commercial Australian television drama is rare and First Nations content makers rarely produce the content we see. Despite a lack of presence on commercial drama platforms there has been, and continues to be, a rich array of First Nations content on Australian public broadcast networks. Content analysis by Screen Australia, the Federal Government agency charged with supporting Australian screen development, production and promotion, aggregates information across the commercial and non-commercial (public broadcasting) platforms which dilutes the non-commercial output. The research presented in this article focused on the systemic processes of commercial Australian television drama production to provide a detailed analysis of the disparity of First Nations content between commercial and non-commercial television. The study engaged with First Nations and non-Indigenous Australian writers, directors, producers, casting agents, casting directors, heads of production, executive producers, broadcast journalists, former channel managers and independent production company executive directors—all exemplars in their fields—to interrogate production processes, script to screen, contributing to inclusion or exclusion of First Nations content in commercial television drama. Our engagement with industry revealed barriers to the inclusion of First Nations stories, and First Nations storytelling, occurring across multiple stages of commercial Australian television drama production.
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7

CHUNG, DONG MYUNG, UN CIG JI, and NOBUAKI OBATA. "QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE." Reviews in Mathematical Physics 14, no. 03 (March 2002): 241–72. http://dx.doi.org/10.1142/s0129055x0200117x.

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White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.
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8

Huang, Zhiyuan. "Quantum white noises—White noise approach to quantum stochastic calculus." Nagoya Mathematical Journal 129 (March 1993): 23–42. http://dx.doi.org/10.1017/s002776300000430x.

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Let H = L2 (R) be the Hilbert space of all complex-valued square integrable functions defined on R, Ф = Γ(H) be the Boson Fock space over H. For each h ∈ H, denote by ε(h) the corresponding exponential vector:in particular ε(0) is the Fock vacuum.
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9

Leggat, Graham. "Making White Noise." Afterimage 18, no. 6 (January 1, 1991): 3–4. http://dx.doi.org/10.1525/aft.1991.18.6.3.

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10

Carter, Steven. "DeLillo's WHITE NOISE." Explicator 58, no. 2 (January 2000): 115–16. http://dx.doi.org/10.1080/00144940009597033.

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11

&NA;. "White Noise [Excerpt]." Academic Medicine 89, no. 9 (September 2014): 1228. http://dx.doi.org/10.1097/acm.0000000000000392.

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12

Grigoriu, Mircea. "White Noise Processes." Journal of Engineering Mechanics 113, no. 5 (January 1987): 757–65. http://dx.doi.org/10.1061/(asce)0733-9399(1987)113:5(757).

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13

Bakalis, Evangelos, Francesca Lugli, and Francesco Zerbetto. "Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions." Fractal and Fractional 7, no. 8 (August 4, 2023): 600. http://dx.doi.org/10.3390/fractalfract7080600.

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White noise is fundamentally linked to many processes; it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise.
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14

Selvaraj, Poovarasan, and E. Chandra. "A variant of SWEMDH technique based on variational mode decomposition for speech enhancement." International Journal of Knowledge-based and Intelligent Engineering Systems 25, no. 3 (November 10, 2021): 299–308. http://dx.doi.org/10.3233/kes-210072.

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In Speech Enhancement (SE) techniques, the major challenging task is to suppress non-stationary noises including white noise in real-time application scenarios. Many techniques have been developed for enhancing the vocal signals; however, those were not effective for suppressing non-stationary noises very well. Also, those have high time and resource consumption. As a result, Sliding Window Empirical Mode Decomposition and Hurst (SWEMDH)-based SE method where the speech signal was decomposed into Intrinsic Mode Functions (IMFs) based on the sliding window and the noise factor in each IMF was chosen based on the Hurst exponent data. Also, the least corrupted IMFs were utilized to restore the vocal signal. However, this technique was not suitable for white noise scenarios. Therefore in this paper, a Variant of Variational Mode Decomposition (VVMD) with SWEMDH technique is proposed to reduce the complexity in real-time applications. The key objective of this proposed SWEMD-VVMDH technique is to decide the IMFs based on Hurst exponent and then apply the VVMD technique to suppress both low- and high-frequency noisy factors from the vocal signals. Originally, the noisy vocal signal is decomposed into many IMFs using SWEMDH technique. Then, Hurst exponent is computed to decide the IMFs with low-frequency noisy factors and Narrow-Band Components (NBC) is computed to decide the IMFs with high-frequency noisy factors. Moreover, VVMD is applied on the addition of all chosen IMF to remove both low- and high-frequency noisy factors. Thus, the speech signal quality is improved under non-stationary noises including additive white Gaussian noise. Finally, the experimental outcomes demonstrate the significant speech signal improvement under both non-stationary and white noise surroundings.
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15

Park, Hyun-Sang. "Gaussian Noise Estimation Using White Noise Test." Journal of Korean Institute of Information Technology 16, no. 4 (April 30, 2018): 51–56. http://dx.doi.org/10.14801/jkiit.2018.16.4.51.

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16

Starosta, William J. "Afrocentric Voice, White Noise." Contemporary Psychology 46, no. 3 (June 2001): 242–44. http://dx.doi.org/10.1037/002478.

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17

Barhoumi, Abdessatar, Habib Ouerdiane, and Anis Riahi. "Pascal white noise calculus." Stochastics 81, no. 3-4 (June 2009): 323–43. http://dx.doi.org/10.1080/17442500902919603.

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18

REDFERN, MYLAN. "COMPLEX WHITE NOISE ANALYSIS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 03 (September 2001): 347–75. http://dx.doi.org/10.1142/s0219025701000541.

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This paper describes a new space, [Formula: see text], of complex Wiener distributions for the analysis of multi-parameter generalized stochastic processes [Formula: see text]. For a certain class of functions [Formula: see text] and complex Wiener integrals Φ1, …, Φm, F(Φ1, …, Φm) is defined as an element of [Formula: see text] and its Fock space decomposition determined.
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19

Accardi, Luigi, and Wided Ayed. "Free white noise flows." Infinite Dimensional Analysis, Quantum Probability and Related Topics 20, no. 03 (September 2017): 1750014. http://dx.doi.org/10.1142/s021902571750014x.

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We extend to free white noise Heisenberg equations the proof of the equivalence between (non-Hamiltonian) stochastic differential equations and Hamiltonian white noise equations. This gives in particular, the microscopic structure of the maps defining free white noise stochastic flows in terms of the free white noise derivations defining them.
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20

Accardi, L., W. Ayed, and H. Ouerdiane. "Module white noise calculus." Random Operators and Stochastic Equations 15, no. 4 (November 2007): 353–86. http://dx.doi.org/10.1515/rose.2007.022.

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21

Allen, William S. "WHITE NOISE, ÉCRITURE BLANCHE." Angelaki 23, no. 3 (May 4, 2018): 28–41. http://dx.doi.org/10.1080/0969725x.2018.1473925.

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22

Frank, David W., Ryan B. Yee, and John Polich. "P3a from white noise." International Journal of Psychophysiology 85, no. 2 (August 2012): 236–41. http://dx.doi.org/10.1016/j.ijpsycho.2012.04.005.

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23

Quastel, Jeremy, and Benedek Valkó. "KdV Preserves White Noise." Communications in Mathematical Physics 277, no. 3 (November 8, 2007): 707–14. http://dx.doi.org/10.1007/s00220-007-0372-6.

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24

Benson, Josef. "Hypermedicalization in White Noise." Journal of Medical Humanities 36, no. 3 (January 24, 2014): 199–215. http://dx.doi.org/10.1007/s10912-014-9271-y.

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25

Crauel, H. "White noise eliminates instability." Archiv der Mathematik 75, no. 6 (December 1, 2000): 472–80. http://dx.doi.org/10.1007/s000130050532.

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26

Ji, Un Cig, Mi Ra Lee, and Peng Cheng Ma. "Generalized Mehler Semigroup on White Noise Functionals and White Noise Evolution Equations." Mathematics 8, no. 6 (June 23, 2020): 1025. http://dx.doi.org/10.3390/math8061025.

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In this paper, we study a representation of generalized Mehler semigroup in terms of Fourier–Gauss transforms on white noise functionals and then we have an explicit form of the infinitesimal generator of the generalized Mehler semigroup in terms of the conservation operator and the generalized Gross Laplacian. Then we investigate a characterization of the unitarity of the generalized Mehler semigroup. As an application, we study an evolution equation for white noise distributions with n-th time-derivative of white noise as an additive singular noise.
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27

Ji, Un Cig. "Evolution systems and continuity equations for white noise functionals." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 101504. http://dx.doi.org/10.1063/5.0073993.

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In this paper, by applying the quantum decomposition of white noise functionals, the continuity equations for white noise functionals are reformulated as time inhomogeneous white noise differential equations. We establish a systematic study of the evolution systems whose infinitesimal generators are quadratic quantum white noises and then, as an application, we study the continuity equations for white noise functionals of which the coefficient has up to the first chaos (Gaussian process). The restriction for the coefficient is comparable (not necessarily equivalent) to the integrability condition of the exponential of the coefficient by Ambrosio and Figalli [J. Funct. Anal. 256, 179–214 (2009)] for the well-posedness of the continuity equation in the abstract Wiener space setting.
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28

Kia, Behnam, Sarvenaz Kia, John F. Lindner, Sudeshna Sinha, and William L. Ditto. "Coupling Reduces Noise: Applying Dynamical Coupling to Reduce Local White Additive Noise." International Journal of Bifurcation and Chaos 25, no. 03 (March 2015): 1550040. http://dx.doi.org/10.1142/s0218127415500406.

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We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices and assume noise is white and additive. Noise from different lattice nodes can diffuse across the lattice and lower the noise level of individual nodes. We develop a theoretical model that explains this observed noise evolution and show how the coupled dynamics can naturally function as an averaging filter. Our numerical simulations are in excellent agreement with the model predictions.
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29

Wang, Xin, Shu-Li Sun, Kai-Hui Ding, and Jing-Yan Xue. "Weighted Measurement Fusion White Noise Deconvolution Filter with Correlated Noise for Multisensor Stochastic Systems." Mathematical Problems in Engineering 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/257619.

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For the multisensor linear discrete time-invariant stochastic control systems with different measurement matrices and correlated noises, the centralized measurement fusion white noise estimators are presented by the linear minimum variance criterion under the condition that noise input matrix is full column rank. They have the expensive computing burden due to the high-dimension extended measurement matrix. To reduce the computing burden, the weighted measurement fusion white noise estimators are presented. It is proved that weighted measurement fusion white noise estimators have the same accuracy as the centralized measurement fusion white noise estimators, so it has global optimality. It can be applied to signal processing in oil seismic exploration. A simulation example for Bernoulli-Gaussian white noise deconvolution filter verifies the effectiveness.
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30

CHEN, J., X. X. YI, H. S. SONG, and L. ZHOU. "NOISE INDUCED ENTANGLEMENT." International Journal of Quantum Information 03, no. 02 (June 2005): 425–33. http://dx.doi.org/10.1142/s0219749905001031.

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We show that two two-level atoms coupled simultaneously with a third dissipated atom would end up with entangled states. The dissipation of the third atom is supposed to come from its coupling to noises with adjustable intensity. Two kinds of noise, white noise and squeezing white noise, are identified to possess the ability to help preparation of entanglement. We confirm that the entanglement is maximized for intermediate values of the noise intensity with all atoms in the ground state, while it is a monotonic function of the spontaneous rates.
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31

Chung, Dong Myung, Un Cig Ji, and Nobuaki Obata. "Higher Powers of Quantum White Noises in Terms of Integral Kernel Operators." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (October 1998): 533–59. http://dx.doi.org/10.1142/s0219025798000296.

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A rigorous mathematical formulation of higher powers of quantum white noises is given on the basis of the most recent theory of white noise distributions due to Cochran, Kuo and Sengupta. The renormalized quantum Itô formula due to Accardi, Lu and Volovich is derived from the renormalized product formula based on integral kernel operators on white noise functions. During the discussion, the analytic characterization of operator symbols and the expansion theorem for a white noise operator in terms of integral kernel operators are established.
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32

Alokaily, Ahmad O., Abdulaziz F. Alqabbani, Adham Aleid, and Khalid Alhussaini. "Toward Accessible Hearing Care: The Development of a Versatile Arabic Word-in-Noise Screening Tool: A Pilot Study." Applied Sciences 12, no. 23 (December 6, 2022): 12459. http://dx.doi.org/10.3390/app122312459.

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Speech-in-noise tests are used to assess the ability of the human auditory system to perceive speech in a noisy environment. Early diagnosis of hearing deficits helps health professionals to plan for the most appropriate management. However, hospitals and auditory clinics have a shortage of reliable Arabic versions of speech-in-noise tests. Additionally, access to specialized healthcare facilities is associated with socioeconomic status. Hence, individuals with compromised socioeconomic status do not have proper access to healthcare. Thus, In the current study, a mobile and cost-effective Arabic speech-in-noise test was developed and tested on 30 normal-hearing subjects, and their ability to perceive words-in-noise was evaluated. Moreover, a comparison between two different background noises was explored (multi-talker babble noise and white noise). The results revealed a significant difference in the thresholds between the two types of background noises. The percent-correct scores ranged from 100% to 54.17% for the white background noise and 91.57% to 50% for the multi-talker babble background noise. The proposed Arabic word-in-noise screening tool has the potential to be used effectively to screen for deteriorated speech perception abilities, particularly in low-resource settings.
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33

Dornic, Stan, and Tarja Laaksonen. "Continuous Noise, Intermittent Noise, and Annoyance." Perceptual and Motor Skills 68, no. 1 (February 1989): 11–18. http://dx.doi.org/10.2466/pms.1989.68.1.11.

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In a within-subjects design, 18 subjects listened to white noise, the intensity of which was controlled by themselves. They were instructed to choose the intensity they experienced as “clearly annoying.” Three kinds of white noise were used: continuous, intermittent regular, and intermittent irregular. In the two intermittent conditions, the proportion of time with the noise on was 50%. The duration of on- and off-periods in the regular condition was 1.15 sec.; in the irregular condition, it varied between 0.25 and 1.65 sec. The subjects chose their “clearly annoying” level three times for each noise type. The results showed that the mean level chosen was 83.9 dB for continuous, 90 dB for intermittent regular, and 89.6 dB for intermittent irregular noise. Pairwise comparisons indicated a significant difference between continuous noise and each of the two intermittent noises while there was no difference between the two intermittent noises. The results are interpreted as indicating that noise-induced annoyance may be a function of the over-all amount of noise rather than the mere presence or absence of intermittency, at least when no concurrent demanding task is performed and when the required annoyance level is set by the subjects themselves. The results further showed that the intensity chosen by the subjects correlated negatively with scores from Weinstein's Noise Sensitivity Scale while the intensity chosen was unrelated to extraversion or neuroticism scores as measured by Eysenck Personality Inventory.
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34

Deon, Aleksei F., Oleg K. Karaduta, and Yulian A. Menyaev. "Phase Congruential White Noise Generator." Algorithms 14, no. 4 (April 5, 2021): 118. http://dx.doi.org/10.3390/a14040118.

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White noise generators can use uniform random sequences as a basis. However, such a technology may lead to deficient results if the original sequences have insufficient uniformity or omissions of random variables. This article offers a new approach for creating a phase signal generator with an improved matrix of autocorrelation coefficients. As a result, the generated signals of the white noise process have absolutely uniform intensities at the eigen Fourier frequencies. The simulation results confirm that the received signals have an adequate approximation of uniform white noise.
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35

Yokoi, Yoshitaka. "Positive generalized white noise functionals." Hiroshima Mathematical Journal 20, no. 1 (1990): 137–57. http://dx.doi.org/10.32917/hmj/1206454446.

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36

Ji, Un-Cig, and Young-Yi Kim. "CONVOLUTIONS OF WHITE NOISE OPERATORS." Bulletin of the Korean Mathematical Society 48, no. 5 (September 30, 2011): 1003–14. http://dx.doi.org/10.4134/bkms.2011.48.5.1003.

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37

Ayed, Wided. "Module Free White Noise Flows." Open Systems & Information Dynamics 25, no. 04 (December 2018): 1850018. http://dx.doi.org/10.1142/s123016121850018x.

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The main result of this paper is to extend to Hilbert module level the proof of the inclusion of (non-Hamiltonian) stochastic differential equations based on free noise into the class of Hamiltonian equations driven by free white noise. To achieve this goal, free white noise calculus is extended to a trivial Hilbert module. The white noise formulation of the Ito table is radically different from the usual Itô tables, both classical and quantum and, combined with the Accardi–Boukas approach to Ito algebra, allows to drastically simplify calculations. Infinitesimal generators of Hilbert module free flows are characterized in terms of stochastic derivations from an initial algebra into a white noise Itô algebra. We prove that any such derivation is the difference of a ⋆-homomorphism and a trivial embedding.
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38

Othman, Hakeem A. "The q-Gamma White Noise." Tatra Mountains Mathematical Publications 66, no. 1 (June 1, 2016): 81–90. http://dx.doi.org/10.1515/tmmp-2016-0022.

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Abstract For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γα,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L2 space with respect to the measure γα,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.
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39

KING, NOEL. "Reading White Noise: floating remarks." Critical Quarterly 33, no. 3 (September 1991): 66–83. http://dx.doi.org/10.1111/j.1467-8705.1991.tb00970.x.

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40

Spencer, J. A., D. J. Moran, A. Lee, and D. Talbert. "White noise and sleep induction." Archives of Disease in Childhood 65, no. 1 (January 1, 1990): 135–37. http://dx.doi.org/10.1136/adc.65.1.135.

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41

Enchev, Ognian B. "White noise indexed by loops." Annals of Probability 26, no. 3 (July 1998): 985–99. http://dx.doi.org/10.1214/aop/1022855741.

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42

Ishihara, Masamichi. "Amplification Induced by White Noise." Progress of Theoretical Physics 116, no. 1 (July 2006): 37–46. http://dx.doi.org/10.1143/ptp.116.37.

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43

Phatak, Sandeep A., Andrew Lovitt, and Jont B. Allen. "Consonant confusions in white noise." Journal of the Acoustical Society of America 124, no. 2 (August 2008): 1220–33. http://dx.doi.org/10.1121/1.2913251.

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44

Onatski, Alexei, and Harald Uhlig. "UNIT ROOTS IN WHITE NOISE." Econometric Theory 28, no. 3 (November 25, 2011): 485–508. http://dx.doi.org/10.1017/s0266466611000636.

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We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T)/p → 0 and p3/T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p, we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as T → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes.
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45

Strain, G. M. "White noise: Pigment-associated deafness." Veterinary Journal 188, no. 3 (June 2011): 247–49. http://dx.doi.org/10.1016/j.tvjl.2010.08.015.

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46

Obata, Nobuaki. "Derivations on white noise functionals." Nagoya Mathematical Journal 139 (September 1995): 21–36. http://dx.doi.org/10.1017/s0027763000005286.

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The Gaussian space (E*, μ) is a natural infinite dimensional analogue of Euclidean space with Lebesgue measure and a special choice of a Gelfand triple gives a fundamental framework of white noise calculus [2] as distribution theory on Gaussian space. It is proved in Kubo-Takenaka [7] that (E) is a topological algebra under pointwise multiplication. The main purpose of this paper is to answer the fundamental question: what are the derivations on the algebra (E)?
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47

Hida, Takeyuki, Ke-Seung Lee, and Sheu-San Lee. "Conformal invariance of white noise." Nagoya Mathematical Journal 98 (June 1985): 87–98. http://dx.doi.org/10.1017/s0027763000021383.

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The remarkable link between the structure of the white noise and that of the infinite dimensional rotation group has been exemplified by various approaches in probability theory and harmonic analysis. Such a link naturally becomes more intricate as the dimension of the time-parameter space of the white noise increases. One of the powerful method to illustrate this situation is to observe the structure of certain subgroups of the infinite dimensional rotation group that come from the diffeomorphisms of the time-parameter space, that is the time change. Indeed, those subgroups would shed light on the probabilistic meanings hidden behind the usual formal observations. Moreover, the subgroups often describe the way of dependency for Gaussian random fields formed from the white noise as the time-parameter runs over the basic parameter space.The main purpose of this note is to introduce finite dimensional subgroups of the infinite dimensional rotation group that have important probabilistic meanings and to discuss their roles in probability theory. In particular, we shall see that the conformal invariance of white noise can be described in terms of the conformal group which is a finite dimensional Lie subgroup of the infinite dimensional rotation group.
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48

Leland, Robert P. "White noise in atmospheric optics." Acta Applicandae Mathematicae 35, no. 1-2 (May 1994): 103–30. http://dx.doi.org/10.1007/bf00994913.

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49

Waldorf, L. "White Noise: Hearing the Disaster." Journal of Human Rights Practice 4, no. 3 (November 1, 2012): 469–74. http://dx.doi.org/10.1093/jhuman/hus025.

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50

Othman, Hakeem. "Generalized free Gaussian white noise." International Journal of Advanced Mathematical Sciences 4, no. 1 (March 27, 2016): 18. http://dx.doi.org/10.14419/ijams.v4i1.5911.

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<p>Based on an adequate new Gel'fand triple, we construct the infinite dimensional free Gaussian white noise measure \(\mu\) using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an \(L^{2}\) space with respect to the measure \(\mu\).</p>
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