117
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

Self-Similarity and Lamperti Transformation for Random Fields

, &
Pages 397-411 | Received 01 Jan 2006, Accepted 01 Feb 2007, Published online: 16 Jul 2007

REFERENCES

  • Ayache , A. ; Leger , S. ; Pontier , M. Drap Brownien fractionnaire . Potential Analysis 2002 , 17 , 31 – 43 .
  • Beran , J. Statistics for Long-Memory Processes ; Chapman & Hall , 1994 .
  • Ehm , W. ; Genton , M.G. ; Gneiting , T. Stationary covariances associated with exponentially convex functions . Bernoulli 2003 , 9 , 607 – 615 .
  • Embrechts , P. ; Maejima , M. Selfsimilar Processes ; Princeton University Press , 2001 .
  • Flandrin , P. ; Borgnat , P. ; Amblard , P.-O. From stationarity to self-similarity, and back: Variations on the Lamperti transformation . In Processes with Long-Range Correlations ; Rangarajan , G. ; Ding , M. , Eds.; Lecture Notes in Physics 621 ; Springer , 2003 ; pp. 88 – 117 .
  • Genton , M.G. ; Perrin , O. On a time deformation reducing nonstationary processes to local stationarity . Journal of Applied Probability 2004 , 41 , 236 – 249 .
  • Gupta , V.K. ; Waymire , E. Multiscaling properties of spatial rainfall and river flow distributions . J. Geophys. Res. 1990 , 95 , 1999 – 2009 .
  • Kiladis , G.N. ; Straub , K.H. ; Haertel , P.T. Zonal and vertical structure of the Madden-Julian oscillation . Journal of the Atmospheric Sciences 2005 , 62 , 2790 – 2809 .
  • Lamperti , J. Semi-stable stochastic processes . Journal of Time Series Analysis 1962 , 9 , 62 – 78 .
  • Loève , M. Fonctions aléatoires à caractère exponentiel . In: Processus Stochastiques et Mouvement Brownien, , 2nd Ed. ; Lévy , P. , Ed. Gauthiers-Villars : Paris ; 1965 , pp. 409 – 420 .
  • Lu , W.Z. ; Wang , X.K. Evolving trend and self-similarity of ozone pollution in central Hong Kong ambient during 1984–2002 . The Science of the Total Environment 2006 , 357 , 160 – 168 .
  • Morata , A. ; Martin , M.L. ; Luna , M.Y. ; Valero , F. Self-similarity patterns of precipitation in the Iberian Peninsula . Journal of Theoretical and Applied Climatology 2006 , 85 , 41 – 59 .
  • Perrin , O. ; Senoussi , R. Reducing non-stationary stochastic processes to stationarity by a time deformation . Statistics and Probability Letters 1999 , 43 , 393 – 397 .
  • Perrin , O. ; Senoussi , R. Reducing non-stationary random fields to stationarity and isotropy using a space deformation . Statistics and Probability Letters 2000 , 48 , 23 – 32 .
  • Samorodnitsky , G. ; Taqqu , M.S. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance ; Chapman & Hall , 1994 .
  • Silverman , R.A. Locally stationary processes . IRE Trans. Inf. Theory 1957 , 3 , 182 – 187 .
  • Taqqu , M.S. Fractional Brownian motion and long-range dependence . In Theory and Applications of Long-Range Dependence ; Doukhan , P. ; Oppenheim , G. ; Taqqu , M.S. , Eds.; Birkhäuser : Boston , 2003 ; pp. 5 – 38 .
  • Waymire , E. Scaling limits and self-similarity in precipitation fields . Water Resources Research 1985 , 21 , 1271 – 1281 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.