Infinitely Divisible Processes
1970; Society for Industrial and Applied Mathematics; Volume: 15; Issue: 1 Linguagem: Inglês
10.1137/1115001
ISSN1095-7219
Autores Tópico(s)Complex Systems and Time Series Analysis
ResumoNext article Infinitely Divisible ProcessesG. MaruyamaG. Maruyamahttps://doi.org/10.1137/1115001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Salomon Bochner, Harmonic analysis and the theory of probability, University of California Press, Berkeley and Los Angeles, 1955viii+176 MR0072370 0068.11702 CrossrefGoogle Scholar[2] Kiyosi Itô, On stochastic processes. I. (Infinitely divisible laws of probability), Jap. J. Math., 18 (1942), 261–301 MR0014629 0060.28908 Google Scholar[3] P. M. Lee, Infinitely divisible stochastic processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 7 (1967), 147–160 10.1007/BF00536328 MR0208668 0167.46301 CrossrefGoogle Scholar[4] Paul Lévy, Processus Stochastiques et Mouvement Brownien. Suivi d'une note de M. Loève, Gauthier-Villars, Paris, 1948, 365– MR0029120 0034.22603 Google Scholar[5] Yasunori Okabe, On Kolmogorov's extension theorem, Sûgaku, 20 (1968), 222–225, (In Japanese.) MR0269795 Google Scholar[6] Gisirô Maruyama, Transformations of flows, J. Math. Soc. Japan, 18 (1966), 303–330 MR0212160 0166.40402 CrossrefGoogle Scholar[7] V. A. Rokhlin, On the basic concepts of measure theory, Mat. Sb., 25 (1949), 107–150, (In Russian.) Google Scholar Next article FiguresRelatedReferencesCited ByDetails Nonsingular Poisson SuspensionsJournal d'Analyse Mathématique, Vol. 146, No. 2 | 11 July 2022 Cross Ref Likelihood theory for the graph Ornstein-Uhlenbeck processStatistical Inference for Stochastic Processes, Vol. 25, No. 2 | 21 October 2021 Cross Ref On operator fractional Lévy motion: integral representations and time-reversibilityAdvances in Applied Probability, Vol. 54, No. 2 | 6 June 2022 Cross Ref Time series with infinite-order partial copula dependenceDependence Modeling, Vol. 10, No. 1 | 23 May 2022 Cross Ref Autocorrelation functions and ergodicity in diffusion with stochastic resettingJournal of Physics A: Mathematical and Theoretical, Vol. 55, No. 10 | 21 February 2022 Cross Ref Asymptotic behavior of dependence measures for Ornstein-Uhlenbeck model based on long memory processesInternational Journal of Advances in Engineering Sciences and Applied Mathematics, Vol. 13, No. 2-3 | 11 October 2021 Cross Ref Asymptotic theory for the detection of mixing in anomalous diffusionJournal of Mathematical Physics, Vol. 62, No. 6 | 1 Jun 2021 Cross Ref Testing of fractional Brownian motion in a noisy environmentChaos, Solitons & Fractals, Vol. 140 | 1 Nov 2020 Cross Ref Measurement instrumentation and selected signal processing techniques for anomalous diffusion analysisMeasurement: Sensors, Vol. 7-9 | 1 Oct 2020 Cross Ref Spectral representations of quasi-infinitely divisible processesStochastic Processes and their Applications, Vol. 130, No. 3 | 1 Mar 2020 Cross Ref Spectral Theory of Dynamical SystemsEncyclopedia of Complexity and Systems Science | 9 June 2020 Cross Ref Dynamical Systems of Probabilistic Origin: Gaussian and Poisson SystemsEncyclopedia of Complexity and Systems Science | 15 December 2020 Cross Ref Mixing Properties of Multivariate Infinitely Divisible Random FieldsJournal of Theoretical Probability, Vol. 32, No. 4 | 1 October 2018 Cross Ref Covariance-based dissimilarity measures applied to clustering wide-sense stationary ergodic processesMachine Learning, Vol. 108, No. 12 | 26 June 2019 Cross Ref Lamperti transformation - Cure for ergodicity breakingCommunications in Nonlinear Science and Numerical Simulation, Vol. 71 | 1 Jun 2019 Cross Ref Representations and isomorphism identities for infinitely divisible processesThe Annals of Probability, Vol. 46, No. 6 | 1 Nov 2018 Cross Ref Polar Decomposition of Scale-Homogeneous Measures with Application to Lévy Measures of Strictly Stable LawsJournal of Theoretical Probability, Vol. 31, No. 3 | 12 April 2017 Cross Ref Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusionNew Journal of Physics, Vol. 20, No. 2 | 8 February 2018 Cross Ref Ergodic properties of Lévy flights coexisting with subdiffusion and related modelsJournal of Mathematical Analysis and Applications, Vol. 458, No. 2 | 1 Feb 2018 Cross Ref The Ambit FrameworkAmbit Stochastics | 2 November 2018 Cross Ref Asymptotic behaviour of time averages for non-ergodic Gaussian processesAnnals of Physics, Vol. 383 | 1 Aug 2017 Cross Ref Selfdecomposable FieldsJournal of Theoretical Probability, Vol. 30, No. 1 | 29 July 2015 Cross Ref Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measureJournal of Applied Probability, Vol. 53, No. 1 | 24 March 2016 Cross Ref Stochastic integral representations and classification of sum- and max-infinitely divisible processesBernoulli, Vol. 22, No. 1 | 1 Feb 2016 Cross Ref EpilogueTempered Stable Distributions | 20 November 2015 Cross Ref Mixed-Norm Spaces and Prediction of S α S Moving AveragesJournal of Time Series Analysis, Vol. 36, No. 6 | 27 April 2015 Cross Ref Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flowsThe Annals of Probability, Vol. 43, No. 1 | 1 Feb 2015 Cross Ref Levy multiplicative chaos and star scale invariant random measuresThe Annals of Probability, Vol. 42, No. 2 | 1 Mar 2014 Cross Ref Gaussian multiplicative chaos and applications: A reviewProbability Surveys, Vol. 11, No. none | 1 Jan 2014 Cross Ref Functional regular variation of Lévy-driven multivariate mixed moving average processesExtremes, Vol. 16, No. 3 | 7 February 2013 Cross Ref Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility modelESAIM: Probability and Statistics, Vol. 17 | 3 June 2013 Cross Ref Ergodic properties of sum- and max-stable stationary random fields via null and positive group actionsThe Annals of Probability, Vol. 41, No. 1 | 1 Jan 2013 Cross Ref Maharam extension and stationary stable processesThe Annals of Probability, Vol. 40, No. 3 | 1 May 2012 Cross Ref Spectral Theory of Dynamical SystemsMathematics of Complexity and Dynamical Systems | 1 Jan 2012 Cross Ref Stationary infinitely divisible processesBrazilian Journal of Probability and Statistics, Vol. 25, No. 3 | 1 Nov 2011 Cross Ref Ergodic properties of anomalous diffusion processesAnnals of Physics, Vol. 326, No. 9 | 1 Sep 2011 Cross Ref Generalization of the Khinchin Theorem to Lévy FlightsPhysical Review Letters, Vol. 105, No. 26 | 23 December 2010 Cross Ref Ergodic properties of max-infinitely divisible processesStochastic Processes and their Applications, Vol. 120, No. 3 | 1 Mar 2010 Cross Ref A Note on Maruyama's Mixing TheoremTheory of Probability & Its Applications, Vol. 54, No. 2 | 21 May 2010AbstractPDF (109 KB)Physical Review E, Vol. 82, No. 1 | 2010 Cross Ref Correlation cascades, ergodic properties and long memory of infinitely divisible processesStochastic Processes and their Applications, Vol. 119, No. 10 | 1 Oct 2009 Cross Ref Random Measures and ApplicationsStochastic Analysis and Applications, Vol. 27, No. 5 | 28 Aug 2009 Cross Ref Poisson suspensions and infinite ergodic theoryErgodic Theory and Dynamical Systems, Vol. 29, No. 02 | 9 December 2008 Cross Ref Spectral Theory of Dynamical SystemsEncyclopedia of Complexity and Systems Science | 1 Jan 2009 Cross Ref Dynamic Interest-Rate Modelling in Incomplete MarketsSSRN Electronic Journal | 1 Jan 2008 Cross Ref Ergodic properties of Poissonian ID processesThe Annals of Probability, Vol. 35, No. 2 | 1 Mar 2007 Cross Ref Infinite Divisibility for Stochastic Processes and Time ChangeJournal of Theoretical Probability, Vol. 19, No. 2 | 24 August 2006 Cross Ref Asymptotic bounds for infinitely divisible sequencesStochastic Processes and their Applications, Vol. 116, No. 11 | 1 Nov 2006 Cross Ref Fractional Ornstein–Uhlenbeck Lévy processes and the Telecom process: Upstairs and downstairsSignal Processing, Vol. 85, No. 8 | 1 Aug 2005 Cross Ref Continuity and Boundedness of Infinitely Divisible Processes: A Poisson Point Process ApproachJournal of Theoretical Probability, Vol. 18, No. 1 | 1 Jan 2005 Cross Ref Large sample theory for statistics of stable moving averagesJournal of Nonparametric Statistics, Vol. 16, No. 3-4 | 31 January 2007 Cross Ref On overload in a storage model, with a self-similar and infinitely divisible inputThe Annals of Applied Probability, Vol. 14, No. 2 | 1 May 2004 Cross Ref A characterization of $\boldsymbol{m}$-dependent stationary infinitely divisible sequences with applications to weak convergenceThe Annals of Probability, Vol. 31, No. 2 | 1 Apr 2003 Cross Ref Skewed α-stable distributions for modelling texturesPattern Recognition Letters, Vol. 24, No. 1-3 | 1 Jan 2003 Cross Ref Long Range Dependence in Heavy Tailed Stochastic ProcessesHandbook of Heavy Tailed Distributions in Finance | 1 Jan 2003 Cross Ref Tail Probabilities of Subadditive Functionals of Lévy ProcessesThe Annals of Applied Probability, Vol. 12, No. 1 | 1 Feb 2002 Cross Ref DEPENDENCE STRUCTURE OF A RENEWAL-REWARD PROCESS WITH INFINITE VARIANCEFractals, Vol. 09, No. 02 | 1 Jun 2001 Cross Ref Ruin probability with claims modeled by a stationary ergodic stable processThe Annals of Probability, Vol. 28, No. 4 | 1 Oct 2000 Cross Ref Likelihood Ratios for ProcessesStochastic Processes | 1 Jan 2000 Cross Ref Ergodicity and fourth-order spectral momentsIEEE Transactions on Information Theory, Vol. 43, No. 4 | 1 Jul 1997 Cross Ref Level crossings of absolutely continuous stationary symmetric $\alpha$-stable processesThe Annals of Applied Probability, Vol. 7, No. 2 | 1 May 1997 Cross Ref Simple conditions for mixing of infinitely divisible processesStochastic Processes and their Applications, Vol. 61, No. 2 | 1 Feb 1996 Cross Ref A characterization of mixing processes of type G1Journal of Theoretical Probability, Vol. 9, No. 1 | 1 Jan 1996 Cross Ref Some mixing conditions for stationary symmetric stable stochastic processesStochastic Processes and their Applications, Vol. 51, No. 2 | 1 Jul 1994 Cross Ref On LIL behaviour for moving averages of some infinitely divisible random measuresStochastic Processes and their Applications, Vol. 49, No. 1 | 1 Jan 1994 Cross Ref Ergodic properties of random measures on stationary sequences of setsStochastic Processes and their Applications, Vol. 46, No. 2 | 1 Jun 1993 Cross Ref Ergodic properties of stationary Poisson sequencesJournal of Computational and Applied Mathematics, Vol. 40, No. 2 | 1 Jun 1992 Cross Ref On path properties of certain infinitely divisible processesStochastic Processes and their Applications, Vol. 33, No. 1 | 1 Oct 1989 Cross Ref Spectral representations of infinitely divisible processesProbability Theory and Related Fields, Vol. 82, No. 3 | 1 Aug 1989 Cross Ref Random fields: Applications in cell biologyStochastic Spatial Processes | 16 September 2006 Cross Ref Stable processes and measures; A surveyProbability Theory on Vector Spaces III | 15 November 2006 Cross Ref Equivalence of measures induced by infinitely divisible processesJournal of Multivariate Analysis, Vol. 13, No. 1 | 1 Mar 1983 Cross Ref Volume 15, Issue 1| 1970Theory of Probability & Its Applications1-162 History Submitted:25 September 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115001Article page range:pp. 1-22ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
Referência(s)