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Wavelets and stochastic processes

https://doi.org/10.1016/s0378-4754(99)00009-9
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37/37 checkable references clean · checked 2026-08-09

Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.

22 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.

The 37 checked references that resolve
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The Time operator of wavelets
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The Laplacian Pyramid as a Compact Image Code
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Multivariate Splines
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An algorithm for the machine calculation of complex Fourier series
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Ergodic Theory
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Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters
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Ten Lectures on Wavelets
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Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data
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Wavelet Transforms and Filter Banks
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Lectures on Computational Fluid Dynamics, Mathematical Physics, and Linear Algebra
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Canonical commutation relations of quantum mechanics and stochastic regularity
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A Hilbert Space Problem Book
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Continuous and Discrete Wavelet Transforms
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Dynamical Systems of Continuous Spectra
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Martingales and Stochastic Integrals
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Wavelets and Dilation Equations: A Brief Introduction
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The 22 references without a DOI — listed, not checked
no DOI — not checkedC. Chiann, P. Morettin, A Wavelet Analysis for Stationary Processes, University of Sao Paulo, Brazil, 1996, preprint
no DOI — not checkedH. Cramer, M. Leadbetter, Stationary and Related Stochastic Processes, Wiley, New York, 1967
no DOI — not checkedJ. Doob, Stochastic Processes, Wiley, New York, 1953
no DOI — not checkedTheory of communication
no DOI — not checkedK. Gustafson, Operator trigonometry of wavelet frames, in: J. Wang, M. Allen, B. Chen, T. Mathew (Eds.), Iterative Methods in Scientific Computation; IMACS Series in Computational and Applied Mathematics 4, New Brunswick, NJ, 1998, pp. 161–166
no DOI — not checkedKolmogorov systems and Haar systems
no DOI — not checkedA. Haar, Zur Theorie der Orthogonalen Functionensystem I, II, Math. Annalen 69 (1910), pp. 38–53; 71 (1911), pp. 331–371
no DOI — not checkedT. Hida, Stationary Stochastic Processes, Princeton University Press, Princeton, NJ, 1970
no DOI — not checkedP. Lax, R. Phillips, Scattering Theory, Academic Press, New York, 1967
no DOI — not checkedG. Mackey, theory of Group Representations, University of Chicago Press, Chicago, 1976
no DOI — not checkedMultiresolution approximations and wavelet orthonormal bases of L2(R)
no DOI — not checkedY. Meyer, Ondelettes et fonctions spline, Seminar EDP, Ecole Polytechnique, Paris, 1986
no DOI — not checkedY. Meyer, Wavelets and Operators, Cambridge University Press, Cambridge, 1992
no DOI — not checkedG. Nason, Wavelet regression by cross-validation, TR 447, Dept. of Statistics, Stanford University, 1994
no DOI — not checkedE. Robinson, Predictive decomposition of time series with application to seismic exploration, MIT GAG Rept. No. 7 (1954); reprinted in, G. Webster (Ed.), Deconvolution, Society of Exploration Geophysicists Tulsa, OK, 1978, pp. 52–118
no DOI — not checkedY. Rozanov, Innovation Processes, Wiley, New York, 1977
no DOI — not checkedB. Sz. Nagy, C. Foias, Harmonic Analysis of Operators in Hilbert Space, North Holland, Amsterdam, 1970
no DOI — not checkedWavelets
no DOI — not checkedP. Walters, Ergodic Theory, Springer Lecture Notes in Math. 458, 1975, Berlin
no DOI — not checkedG. Webster (Ed.), Deconvolution, Society of Exploration Geophysics, Tulsa, OK, 1978
no DOI — not checkedJ. Pham, Unilateral shifts in wavelet theory and algorithm, in Abstracts, 1st International Conference on Semigroups of Operators: Theory and Applications, Newport Beach, CA, 14–18 December 1998, p. 34; also see J. Pham, dissertation, electrical engineering, UCLA, 1999 (to appear)
no DOI — not checkedK. Gustafson, Wavelets as stochastic processes, in M. Kobayashi, S. Sakakibara, M. Yamada (Eds.), Proc. Workshop on Wavelets and Wavelet-based Technologies, Tokyo, Japan, 29–30 October 1998, IBM Japan/University of Tokyo, 1998, pp. 40–43
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