Simulation example of a black noise

Tsirelson and Vershik (In Rev Math Phys 10(1):81–145, 1998) introduced the notion of a mathematical noise, which possesses completely opposite properties to those of a white noise. Afterward, Tsirelson (In Lectures on probability theory and statistics, Lecture Notes in Math., 1840, Springer, Berlin,...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2024, Vol.41 (1), p.191-210
Main Authors: Amaba, T., Aoyama, T., Araki, S., Eguchi, S.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Artificial neural networks
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Original Paper
Probability theory
White noise
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Summary:Tsirelson and Vershik (In Rev Math Phys 10(1):81–145, 1998) introduced the notion of a mathematical noise, which possesses completely opposite properties to those of a white noise. Afterward, Tsirelson (In Lectures on probability theory and statistics, Lecture Notes in Math., 1840, Springer, Berlin, pp 1–106, 2004) called this noise: ‘black noise.’ In this paper, we provide a method to simulate black noise using a modified Bayesian convolutional neural network. Then we study the behavior of black noise both numerically and visually.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-023-00594-7