The Hausdorff Dimension of the Level Sets for a Fractional Brownian Sheet

References

• Adler , R.J. 1978 . The uniform dimension of the level sets of a Brownian sheet . Ann. Probab. , 6 : 509 – 515 .
   Web of Science ®Google Scholar
• Adler , R.J. 1981 . The Geometry of Random Fields New York , , Singapore : Wiley .
   Google Scholar
• Cuzick , J. and Du Peez , J. 1982 . Joint continuity of Gaussian local times . Ann. Probab. , 10 : 810 – 817 .
   Web of Science ®Google Scholar
• Ehm , W. 1981 . Sample function properties of multi-parameter stable process . Z. Wahrsch. Verw. Gebiete , 56 : 195 – 228 . [CROSSREF]
   Web of Science ®Google Scholar
• Geman , D. and Horowitz , J. 1980 . Occupation densities . Ann. Probab. , 8 : 1 – 67 .
   Web of Science ®Google Scholar
• Geman , D. , Horowitz , J. and Rosen , J. 1984 . A local time analysis of intersections of Brownian paths in the plane . Ann. Probab. , 12 : 86 – 107 .
   Web of Science ®Google Scholar
• Khoshnevisan , D. and Xiao , Y.M. 2002 . Lever set of additive Lévy processes . Ann. Probab. , 27 : 62 – 100 .
   Google Scholar
• Mason , D.M. and Shi , Z. 2001 . Small deviations for some multi-parameter Gaussian processes . J. Theo. Probab. , 14 : 213 – 239 . [CROSSREF]
   Web of Science ®Google Scholar
• Marcus , M.B. and Shepp , L.A. 1972 . “ Sample behavior of Gaussian processes. ” . In Proc. sixth Berkeley Symp. Math. Statist. Probab. 423 – 441 . Berkeley , , Singapore : University of California Press .
   Google Scholar
• Perkins , E. 1981 . The exact Hausdorff measure of the level set of Brownian motion . Z. Wahrsch. Verw. Gebiete , 58 : 373 – 388 . [CROSSREF]
   Web of Science ®Google Scholar
• Pitt , L.D. 1978 . Local times for Gaussian vector fields . Indiana Univ. Math. J. , 27 : 309 – 330 .
   Web of Science ®Google Scholar
• Rosen , J. 1984 . Self-intersections of random fields . Ann. Probab. , 12 : 108 – 119 .
   Web of Science ®Google Scholar
• Taylor , S.J. and Wendel , J.G. 1966 . The exact Hausdorff measure of the level set of a stable process . Z. Wahrsch. Verw. Gebiete , 6 : 170 – 180 . [CROSSREF]
   Google Scholar
• Xiao , Y.M. 1997 . Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields . Probab. Theory Relat. Fields , 109 : 129 – 157 . [CROSSREF]
   Web of Science ®Google Scholar
• Xiao , Y.M. and Zhang , T.S. 2002 . Local times of fractional Brownian sheets . Probab. Theory Relat. Fields , 124 : 204 – 226 . [CROSSREF]
   Web of Science ®Google Scholar