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Volumn 13, Issue 1, 2007, Pages 1-37

Geometric properties of fractional Brownian sheets

Author keywords

Fourier dimension; Fractional Brownian sheet; Hausdorff dimension; Image; Local times; Salem set; Sectorial local nondeterminism

Indexed keywords


EID: 33846996313     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-005-5078-y     Document Type: Article
Times cited : (62)

References (50)
  • 1
    • 4043116925 scopus 로고    scopus 로고
    • Hausdorff dimension of the graph of the fractional Brownian sheet
    • Ayache, A. (2004). Hausdorff dimension of the graph of the fractional Brownian sheet, Rev. Mat. Iberoamericana 20, 395-412.
    • (2004) Rev. Mat. Iberoamericana , vol.20 , pp. 395-412
    • Ayache, A.1
  • 3
    • 0742306489 scopus 로고    scopus 로고
    • Rate optimality of wavelet series approximations of fractional Brownian sheet
    • Ayache, A. and Taqqu, M. S. (2003). Rate optimality of wavelet series approximations of fractional Brownian sheet, J. Fourier Anal. Appl. 9(5), 451-471.
    • (2003) J. Fourier Anal. Appl , vol.9 , Issue.5 , pp. 451-471
    • Ayache, A.1    Taqqu, M.S.2
  • 4
    • 33846994797 scopus 로고    scopus 로고
    • Joint continuity of the local times of fractional Brownian sheets
    • to appear
    • Ayache, A., Wu, D., and Xiao, Y. (2006). Joint continuity of the local times of fractional Brownian sheets, Ann. Inst. H. Poincaré Probab. Statist., to appear.
    • (2006) Ann. Inst. H. Poincaré Probab. Statist
    • Ayache, A.1    Wu, D.2    Xiao, Y.3
  • 5
    • 23944466359 scopus 로고    scopus 로고
    • Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets
    • Ayache, A. and Xiao, Y. (2005). Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, J. Fourier Anal. Appl. 11(4), 407-439.
    • (2005) J. Fourier Anal. Appl , vol.11 , Issue.4 , pp. 407-439
    • Ayache, A.1    Xiao, Y.2
  • 6
    • 0141688191 scopus 로고    scopus 로고
    • Small ball probabilities of fractional Brownian sheets via fractional integration operators
    • Belinski, E. and Linde, W. (2002). Small ball probabilities of fractional Brownian sheets via fractional integration operators, J. Theoret. Probab. 15, 589-612.
    • (2002) J. Theoret. Probab , vol.15 , pp. 589-612
    • Belinski, E.1    Linde, W.2
  • 8
  • 9
    • 0002807832 scopus 로고
    • Local nondeterminism and local times of Gaussian processes
    • Berman, S. M. (1973). Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23, 69-94.
    • (1973) Indiana Univ. Math. J , vol.23 , pp. 69-94
    • Berman, S.M.1
  • 11
    • 0041350470 scopus 로고    scopus 로고
    • Anisotropic analysis of some Gaussian models
    • Bonami, A. and Estrade, A. (2003). Anisotropic analysis of some Gaussian models, J. Fourier Anal. Appl. 9(3), 215-236.
    • (2003) J. Fourier Anal. Appl , vol.9 , Issue.3 , pp. 215-236
    • Bonami, A.1    Estrade, A.2
  • 12
    • 0013264235 scopus 로고
    • Joint continuity of Gaussian local times
    • Cuzick, J. and DuPreez, J. (1982). Joint continuity of Gaussian local times, Ann. Probab. 10, 810-817.
    • (1982) Ann. Probab , vol.10 , pp. 810-817
    • Cuzick, J.1    DuPreez, J.2
  • 13
    • 0033474256 scopus 로고    scopus 로고
    • Fractal analysis of surface roughness by using spatial data (with discussion)
    • Davies, S. and Hall, P. (1999). Fractal analysis of surface roughness by using spatial data (with discussion), J. Roy. Statist. Soc. Ser. B 61, 3-37.
    • (1999) J. Roy. Statist. Soc. Ser. B , vol.61 , pp. 3-37
    • Davies, S.1    Hall, P.2
  • 14
    • 0034563536 scopus 로고    scopus 로고
    • Estimates for the small ball probabilities of the fractional Brownian sheet
    • Dunker, T. (2000). Estimates for the small ball probabilities of the fractional Brownian sheet, J. Theoret. Probab. 13, 357-382.
    • (2000) J. Theoret. Probab , vol.13 , pp. 357-382
    • Dunker, T.1
  • 15
    • 14544268596 scopus 로고    scopus 로고
    • Optimality of an explicit series of the fractional Browinan sheet
    • Dzhaparidze, K. and van Zanten, H. (2005). Optimality of an explicit series of the fractional Browinan sheet, Statist. Probab. Lett. 71, 295-301.
    • (2005) Statist. Probab. Lett , vol.71 , pp. 295-301
    • Dzhaparidze, K.1    van Zanten, H.2
  • 16
    • 0036787612 scopus 로고    scopus 로고
    • On the most visited sites of symmetric Markov processes
    • Eisenbaum, N. and Khoshnevisan, D. (2002). On the most visited sites of symmetric Markov processes, Stoch. Process. Appl. 101, 241-256.
    • (2002) Stoch. Process. Appl , vol.101 , pp. 241-256
    • Eisenbaum, N.1    Khoshnevisan, D.2
  • 18
    • 0001290826 scopus 로고
    • Continuity properties of Gaussian processes with multidimensional time parameter
    • California, Berkeley, CA, /, Univ. California Press, Berkeley. 1972
    • Garsia, A. M. (1972). Continuity properties of Gaussian processes with multidimensional time parameter, Proc. 6th Berkeley Symp. Math. Statist. Probability, (Univ. California, Berkeley, CA, 1970/1971), II, 369-374, Univ. California Press, Berkeley.
    • (1970) Proc. 6th Berkeley Symp. Math. Statist. Probability, (Univ , vol.2 , pp. 369-374
    • Garsia, A.M.1
  • 19
    • 0002902384 scopus 로고
    • Occupation densities
    • Geman, D. and Horowitz, J. (1980). Occupation densities, Ann. Probab. 8, 1-67.
    • (1980) Ann. Probab , vol.8 , pp. 1-67
    • Geman, D.1    Horowitz, J.2
  • 20
    • 14944346629 scopus 로고    scopus 로고
    • From N parameter fractional Brownian motions to N parameter multifractional Brownian motions
    • to appear
    • Herbin, E. (2002). From N parameter fractional Brownian motions to N parameter multifractional Brownian motions, Rocky Mount. J. Math., to appear.
    • (2002) Rocky Mount. J. Math
    • Herbin, E.1
  • 23
    • 18844399143 scopus 로고
    • Ensembles aléatoires et dimensions
    • El Escorial, North-Holland, Amsterdam
    • Kahane, J.-P. (1985). Ensembles aléatoires et dimensions, in, Recent Progress in Fourier Analysis, (El Escorial, 1983), 65-121, North-Holland, Amsterdam.
    • (1983) Recent Progress in Fourier Analysis , pp. 65-121
    • Kahane, J.-P.1
  • 24
    • 0342810469 scopus 로고
    • Fractals and random measures
    • Kahane, J.-P. (1993). Fractals and random measures, Bull. Sci. Math. 117, 153-159.
    • (1993) Bull. Sci. Math , vol.117 , pp. 153-159
    • Kahane, J.-P.1
  • 26
    • 0000176104 scopus 로고    scopus 로고
    • On the fractional anisotropic Wiener field
    • Kamont, A. (1996). On the fractional anisotropic Wiener field, Probab. Math. Statist. 16, 85-98.
    • (1996) Probab. Math. Statist , vol.16 , pp. 85-98
    • Kamont, A.1
  • 27
    • 33751397281 scopus 로고
    • Fourier analysis and paths of Brownian motion
    • Kaufman, R. (1975). Fourier analysis and paths of Brownian motion, Bull. Soc. Math. France 103, 427-432.
    • (1975) Bull. Soc. Math. France , vol.103 , pp. 427-432
    • Kaufman, R.1
  • 28
    • 33748947145 scopus 로고    scopus 로고
    • Sectorial local nondeterminism and the geometry of the Brownian sheet
    • Khoshnevisan, D., Wu, D., and Xiao, Y. (2006). Sectorial local nondeterminism and the geometry of the Brownian sheet, Electron. J. Probab. 11, 817-843.
    • (2006) Electron. J. Probab , vol.11 , pp. 817-843
    • Khoshnevisan, D.1    Wu, D.2    Xiao, Y.3
  • 30
    • 0141643497 scopus 로고    scopus 로고
    • Optimal series representation of fractional Brownian sheet
    • Kühn, T. and Linde, W. (2002). Optimal series representation of fractional Brownian sheet, Bernoulli 8, 669-696.
    • (2002) Bernoulli , vol.8 , pp. 669-696
    • Kühn, T.1    Linde, W.2
  • 31
    • 0000501589 scopus 로고
    • Fractional Brownian motion, fractional noises and applications
    • Mandelbrot, B. and Van Ness, J. (1968). Fractional Brownian motion, fractional noises and applications, SIAM Rev. 10, 422-437.
    • (1968) SIAM Rev , vol.10 , pp. 422-437
    • Mandelbrot, B.1    Van Ness, J.2
  • 32
    • 0042786029 scopus 로고    scopus 로고
    • Small deviations for some multi-parameter Gaussian processes
    • Mason, D. M. and Shi, Z. (2001). Small deviations for some multi-parameter Gaussian processes, J. Theoret. Probab. 14, 213-239.
    • (2001) J. Theoret. Probab , vol.14 , pp. 213-239
    • Mason, D.M.1    Shi, Z.2
  • 34
    • 0034556365 scopus 로고    scopus 로고
    • Salem sets and restriction properties of Fourier transforms
    • Mockenhaupt, G. (2000). Salem sets and restriction properties of Fourier transforms, Geom. Funct. Anal. 10, 1579-1587.
    • (2000) Geom. Funct. Anal , vol.10 , pp. 1579-1587
    • Mockenhaupt, G.1
  • 35
    • 0043228684 scopus 로고
    • Uniform dimension results for the Brownian sheet
    • Mountford, T. S. (1989). Uniform dimension results for the Brownian sheet, Ann. Probab. 17, 1454-1462.
    • (1989) Ann. Probab , vol.17 , pp. 1454-1462
    • Mountford, T.S.1
  • 36
    • 2142709565 scopus 로고    scopus 로고
    • Hitting probabilities of a random string
    • Mueller, C. and Tribe, R. (2002). Hitting probabilities of a random string, Electron. J. Probab. 7(10), 1-29.
    • (2002) Electron. J. Probab , vol.7 , Issue.10 , pp. 1-29
    • Mueller, C.1    Tribe, R.2
  • 37
    • 33846949049 scopus 로고    scopus 로고
    • Stochastic heat equation driven by fractional noise
    • preprint
    • Nualart, D. (2006). Stochastic heat equation driven by fractional noise, preprint.
    • (2006)
    • Nualart, D.1
  • 38
    • 0000471777 scopus 로고    scopus 로고
    • Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations
    • Øksendal, B. and Zhang, T. (2000). Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations, Stoch. Stoch. Rep. 71, 141-163.
    • (2000) Stoch. Stoch. Rep , vol.71 , pp. 141-163
    • Øksendal, B.1    Zhang, T.2
  • 39
    • 0001564922 scopus 로고
    • Local times for Gaussian vector fields
    • Pitt, L. D. (1978). Local times for Gaussian vector fields, Indiana Univ. Math. J. 27, 309-330.
    • (1978) Indiana Univ. Math. J , vol.27 , pp. 309-330
    • Pitt, L.D.1
  • 41
    • 33751433580 scopus 로고    scopus 로고
    • Images of Gaussian random fields: Salem sets and interior points
    • Shieh, N. and Xiao, Y. (2006). Images of Gaussian random fields: Salem sets and interior points, Stud. Math. 176, 37-60.
    • (2006) Stud. Math , vol.176 , pp. 37-60
    • Shieh, N.1    Xiao, Y.2
  • 42
    • 84971877468 scopus 로고
    • Two definitions of fractional dimension
    • Tricot, C. (1982). Two definitions of fractional dimension, Math. Proc. Cambridge Phil. Soc. 91, 57-74.
    • (1982) Math. Proc. Cambridge Phil. Soc , vol.91 , pp. 57-74
    • Tricot, C.1
  • 44
    • 0039710539 scopus 로고    scopus 로고
    • Hausdorff measure of the sample paths of Gaussian random fields
    • Xiao, Y. (1996). Hausdorff measure of the sample paths of Gaussian random fields, Osaka J. Math. 33, 895-913.
    • (1996) Osaka J. Math , vol.33 , pp. 895-913
    • Xiao, Y.1
  • 45
    • 0031574846 scopus 로고    scopus 로고
    • Packing dimension of the image of fractional Brownian motion
    • Xiao, Y. (1997). Packing dimension of the image of fractional Brownian motion, Statist. Probab. Lett. 33, 379-387.
    • (1997) Statist. Probab. Lett , vol.33 , pp. 379-387
    • Xiao, Y.1
  • 46
    • 33846986040 scopus 로고    scopus 로고
    • Properties of local nondeterminism of Gaussian and stable random fields and their applications
    • Xiao, Y. (2006). Properties of local nondeterminism of Gaussian and stable random fields and their applications, Ann. Fac. Sci. Toulouse Math. XV, 157-193.
    • (2006) Ann. Fac. Sci. Toulouse Math , vol.15 , pp. 157-193
    • Xiao, Y.1
  • 47
    • 51849089017 scopus 로고    scopus 로고
    • Strong local nondeterminism and sample path properties of Gaussian random fields
    • submitted
    • Xiao, Y. (2006). Strong local nondeterminism and sample path properties of Gaussian random fields, submitted.
    • (2006)
    • Xiao, Y.1
  • 48
    • 34547591403 scopus 로고    scopus 로고
    • Sample path properties of anisotropic Gaussian random fields
    • in preparation
    • Xiao, Y. (2006). Sample path properties of anisotropic Gaussian random fields, in preparation.
    • (2006)
    • Xiao, Y.1
  • 49
    • 0035981340 scopus 로고    scopus 로고
    • Local times of fractional Brownian sheets
    • Xiao, Y. and Zhang, T. (2002). Local times of fractional Brownian sheets, Probab. Theory Relat. Fields 124, 204-226.
    • (2002) Probab. Theory Relat. Fields , vol.124 , pp. 204-226
    • Xiao, Y.1    Zhang, T.2
  • 50
    • 84953751498 scopus 로고
    • Cambridge University Press, Cambridge
    • Zygmund, A. (1959). Trigonometric Series, Vol. I, Cambridge University Press, Cambridge.
    • (1959) Trigonometric Series , vol.1
    • Zygmund, A.1


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