Some Results Concerning the Zero-Crossings of Gaussian Noise
Eugene H. Wong · SIAM Journal on Applied Mathematics · 1966
Previous article Next article Some Results Concerning the Zero-Crossings of Gaussian NoiseE. WongE. Wonghttps://doi.org/10.1137/0114099PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J., 41 (1962), 463–501 MR0133183 (24:A3017) CrossrefISIGoogle Scholar[2] David Slepian, M. Rosenblatt, On the zeros of Gaussian noiseProc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, 104–115 MR0148128 (26:5636) 0139.34101 Google Scholar[3] M. S. Longuet-Higgins, Bounding approximations to the distribution of intervals between zeros of a stationary gaussian processProc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, 63–88 MR0148124 (26:5633) 0142.14002 Google Scholar[4] Mark Kac and , David Slepian, Large excursions of Gaussian processes, Ann. Math. Statist., 30 (1959), 1215–1228 MR0115222 (22:6024) 0089.34101 CrossrefISIGoogle Scholar[5] H. P. McKean, Jr., A winding problem for a resonator driven by a white noise, J. Math. Kyoto Univ., 2 (1963), 227–235 MR0156389 (27:6312) 0119.34701 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Evenly brightening using kurtosis Gaussian pattern to simplify image binarizationJournal of Physics: Conference Series, Vol. 1397, No. 1 Cross Ref Lacunarity of the zero crossings of Gaussian processes5 June 2019 | Physical Review E, Vol. 99, No. 6 Cross Ref Gaussian Integrals and Rice Series in Crossing Distributions—to Compute the Distribution of Maxima and Other Features of Gaussian ProcessesStatistical Science, Vol. 34, No. 1 Cross Ref Periodicity in the autocorrelation function as a mechanism for regularly occurring zero crossings or extreme values of a Gaussian process18 December 2017 | Physical Review E, Vol. 96, No. 6 Cross Ref Persistence Probabilities and Exponents Cross Ref The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes7 July 2014 Cross Ref References Cross Ref A Langevin process reflected at a partially elastic boundary: IStochastic Processes and their Applications, Vol. 122, No. 1 Cross Ref Using mean reversion as a measure of persistenceEconomic Modelling, Vol. 27, No. 1 Cross Ref References and Suggested Reading21 July 2008 Cross Ref Crossing intervals of non-Markovian Gaussian processes23 July 2008 | Physical Review E, Vol. 78, No. 1 Cross Ref Fluctuations in the zeros of differentiable Gaussian processes11 March 2008 | Physical Review E, Vol. 77, No. 3 Cross Ref The ARHD modelJournal of Statistical Planning and Inference, Vol. 137, No. 2 Cross Ref RECENT DEVELOPMENTS ON LOWER TAIL PROBABILITIES FOR GAUSSIAN PROCESSES25 January 2012 | COSMOS, Vol. 01, No. 01 Cross Ref Local Hölder exponent estimation for multivariate continuous time processesJournal of Nonparametric Statistics, Vol. 16, No. 1-2 Cross Ref Optimal sampling for density estimation in continuous time21 February 2003 | Journal of Time Series Analysis, Vol. 24, No. 1 Cross Ref The one-sided barrier problem for an integrated ornstein-uhlenbeck processCommunications in Statistics. 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Wong31 July 2006 | SIAM Journal on Applied Mathematics, Vol. 18, No. 1AbstractPDF (435 KB)An Upper Bound on the Zero-Crossing Distribution*29 July 2013 | Bell System Technical Journal, Vol. 47, No. 4 Cross Ref Approximate and Exact Results Concerning Zeros of Gaussian Noise29 July 2013 | Bell System Technical Journal, Vol. 47, No. 3 Cross Ref Volume 14, Issue 6| 1966SIAM Journal on Applied Mathematics History Submitted:26 July 1965Accepted:31 January 1966Published online:01 August 2006 InformationCopyright © 1966 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0114099Article page range:pp. 1246-1254ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics