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Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes

1965; Society for Industrial and Applied Mathematics; Volume: 7; Issue: 1 Linguagem: Inglês

10.1137/1007007

1095-7200

Joel Franklin,

Scientific Research and Discoveries

Previous article Next article Numerical Simulation of Stationary and Non-Stationary Gaussian Random ProcessesJoel N. FranklinJoel N. Franklinhttps://doi.org/10.1137/1007007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 (15,445b) 0053.26802 Google Scholar[2] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956x+511 MR0075670 (17,788d) 0070.12401 Google Scholar[3] Wilbur B. Davenport, Jr. and , William L. Root, An introduction to the theory of random signals and noise, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1958ix+393 MR0092275 (19,1090b) 0198.24002 Google Scholar[4] R. B. Blackman and , J. W. Tukey, The measurement of power spectra: From the point of view of communications engineering, Dover Publications Inc., New York, 1959x+190 MR0102899 (21:1684) 0084.21703 Google Scholar[5] F. R. Gantmacher, The theory of matrices. Vols. 1, 2, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959Vol. 1, x+374 pp. Vol. 2, ix+276 MR0107649 (21:6372c) Google Scholar[6] Joel N. Franklin, Deterministic simulation of random processes, Math. Comp., 17 (1963), 28–59 MR0149640 (26:7125) 0124.34601 CrossrefGoogle Scholar[7] Hermann Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann., 77 (1916), 313–352 10.1007/BF01475864 MR1511862 CrossrefGoogle Scholar[8] Joel N. Franklin, The covariance matrix of a continuous autoregressive vector time-series, Ann. Math. Statist., 34 (1963), 1259–1264 MR0155363 (27:5297) 0139.37002 CrossrefISIGoogle Scholar[9] G. E. P. Box and , Mervin E. Muller, A note on the generation of random normal deviates, Ann. Math. Statist., 29 (1958), 610–611 0085.13720 CrossrefISIGoogle Scholar[10] T. E. Hull and , A. R. Dobell, Random number generators, SIAM Rev., 4 (1962), 230–254 10.1137/1004061 MR0148202 (26:5710) 0111.14701 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Postprocessing subtraction of tilt-to-length noise in LISA15 August 2022 | Physical Review D, Vol. 106, No. 4 Cross Ref Constructing Oscillating Function-Based Covariance Matrix to Allow Negative Correlations in Gaussian Random Field Models for Uncertainty Quantification3 March 2020 | Journal of Mechanical Design, Vol. 142, No. 7 Cross Ref Comparison of Spacewise and Timewise Methods for GRACE Gravity Field Recovery17 August 2019 Cross Ref History of uniform random number generation Cross Ref Instrument data simulations for GRACE Follow-on: observation and noise models17 November 2017 | Earth System Science Data, Vol. 9, No. 2 Cross Ref Gravity for Detecting Caves: Airborne and Terrestrial Simulations Based on a Comprehensive Karstic Cave Benchmark11 October 2015 | Pure and Applied Geophysics, Vol. 173, No. 4 Cross Ref Coherent states formulation of polymer field theoryThe Journal of Chemical Physics, Vol. 140, No. 2 Cross Ref Supplementary References30 November 2013 Cross Ref Assessment of Load Extrapolation Methods for Wind Turbines23 February 2011 | Journal of Solar Energy Engineering, Vol. 133, No. 2 Cross Ref Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation5 August 2010 | Physical Review D, Vol. 82, No. 4 Cross Ref A spectral-based Monte Carlo algorithm for generating samples of nonstationary Gaussian processesMonte Carlo Methods and Applications, Vol. 16, No. 2 Cross Ref Subtraction-noise projection in gravitational-wave detector networks23 June 2008 | Physical Review D, Vol. 77, No. 12 Cross Ref Adaptive tuning of elasto-plastic damperInternational Journal of Non-Linear Mechanics, Vol. 42, No. 7 Cross Ref Gaussian processes and neuronal modeling30 September 2006 | Natural Computing, Vol. 6, No. 3 Cross Ref Gaussian Processes and Neuronal Modeling Cross Ref Computational Methods for the Evaluation of Neuron’s Firing Densities Cross Ref Correlational and distributional effects in network traffic modelsPerformance Evaluation, Vol. 44, No. 1-4 Cross Ref Simulation of Gaussian Processes and First Passage Time Densities Evaluation Cross Ref On a non-Markov neuronal model and its approximationsBiosystems, Vol. 48, No. 1-3 Cross Ref Vectorized simulations of normal processes for first crossing-time problems9 June 2005 Cross Ref Response statistics of nonlinear, compliant offshore structures by the path integral solution methodProbabilistic Engineering Mechanics, Vol. 8, No. 2 Cross Ref Non-homogeneous track-induced response of vehicles with non-linear suspension during variable velocity runsJournal of Sound and Vibration, Vol. 143, No. 1 Cross Ref Simulation of stochastic loads for fatigue experimentsExperimental Mechanics, Vol. 29, No. 2 Cross Ref Generation of a time series having a specified power spectrum with minimum roundoff noiseIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 37, No. 4 Cross Ref Turbulence spectra from individual realization laser velocimetry dataExperiments in Fluids, Vol. 3, No. 1 Cross Ref References Cross Ref Generation of a random sequence having a jointly specified marginal distribution and autocovarianceIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 30, No. 6 Cross Ref An approximation of random field with a bounded discrete parameter spaceMathematics and Computers in Simulation, Vol. 22, No. 4 Cross Ref Numerical Generation Methods of Homogeneous and Nonhomogeneous Two-Dimensional Gaussian Random FieldsZ. 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