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Volumn 359, Issue 7, 2007, Pages 3125-3151

Images of the brownian sheet

Author keywords

Bessel riesz capacity; Brownian sheet; Hausdorff dimension; Image; Interior point

Indexed keywords


EID: 53349094273     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-04073-1     Document Type: Article
Times cited : (32)

References (25)
  • 2
    • 0013309115 scopus 로고
    • Correction to: The uniform dimension of the level sets of a brownian sheet
    • Correction to: "The uniform dimension of the level sets of a Brownian sheet" [Ann. Probab. 6 (1978), no.3, 509-515]
    • (1978) Ann. Probab. , vol.6 , Issue.3 , pp. 509-515
  • 3
    • 77950949540 scopus 로고
    • MR0600348 (82h:60148)
    • Ann. Probab. 8(5) (1980), 1001-1002. MR0600348 (82h:60148)
    • (1980) Ann. Probab. , vol.8 , Issue.5 , pp. 1001-1002
  • 4
    • 0013309115 scopus 로고
    • The uniform dimension of the level sets of a Brownian sheet
    • MR0490818 (80a:60102)
    • The uniform dimension of the level sets of a Brownian sheet, Ann. Probab. 6(3) (1978), 509-515. MR0490818 (80a:60102)
    • (1978) Ann. Probab. , vol.6 , Issue.3 , pp. 509-515
  • 5
    • 0009095592 scopus 로고
    • Stochastic integrals in the plane
    • MR0420845 (54:8857)
    • R. Cairoli and John B. Walsh, Stochastic integrals in the plane, Acta Math. 134 (1977), 111-183. MR0420845 (54:8857)
    • (1977) Acta Math. , vol.134 , pp. 111-183
    • Cairoli, R.1    Walsh, J.B.2
  • 6
    • 0013264235 scopus 로고
    • Joint continuity of Gaussian local times
    • MR0659550 (83f:60061)
    • Jack Cuzick and Johannes P. DuPreez, Joint continuity of Gaussian local times, Ann. Probab. 10(3) (1982), 810-817. MR0659550 (83f:60061)
    • (1982) Ann. Probab. , vol.10 , Issue.3 , pp. 810-817
    • Cuzick, J.1    DuPreez, J.P.2
  • 7
    • 0001287276 scopus 로고
    • Sample function properties of multiparameter stable processes
    • MR0618272 (82g:60096)
    • W. Ehm, Sample function properties of multiparameter stable processes, Z. Wahrsch. Verw. Gebiete 56(2) (1981), 195-228. MR0618272 (82g:60096)
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , Issue.2 , pp. 195-228
    • Ehm, W.1
  • 8
    • 0003840368 scopus 로고
    • John Wiley & Sons Ltd., Chichester, MR1102677 (92j:28008)
    • Kenneth Falconer, Fractal Geometry, John Wiley & Sons Ltd., Chichester, 1990. MR1102677 (92j:28008)
    • (1990) Fractal Geometry
    • Falconer, K.1
  • 9
    • 0002902384 scopus 로고
    • Occupation densities
    • MR0556414 (81b:60076)
    • Donald Geman and Joseph Horowitz, Occupation densities, Ann. Probab. 8(1) (1980), 1-67. MR0556414 (81b:60076)
    • (1980) Ann. Probab. , vol.8 , Issue.1 , pp. 1-67
    • Geman, D.1    Horowitz, J.2
  • 10
    • 0005481098 scopus 로고
    • Local properties of some gaussian processes
    • MR0458559 (56:16759)
    • John Hawkes, Local properties of some Gaussian processes, Z.Wahrscheinlichkeitstheorie und Verw. Gebiete 40(4) (1977), 309-315. MR0458559 (56:16759)
    • (1977) Z.Wahrscheinlichkeitstheorie und Verw. Gebiete , vol.40 , Issue.4 , pp. 309-315
    • Hawkes, J.1
  • 11
    • 0003851494 scopus 로고
    • Second Edition, Cambridge University Press, Cambridge MR0833073 (87m:60119)
    • Jean-Pierre Kahane, Some Random Series of Functions, Second Edition, Cambridge University Press, Cambridge, 1985a. MR0833073 (87m:60119)
    • (1985) Some Random Series of Functions
    • Kahane, J.-P.1
  • 12
    • 77950930076 scopus 로고
    • Recent progress in Fourier analysis (El Escorial, 1983 65-121, North-Holland, Amsterdam MR0848143 (87k:60110)
    • Ensembles aléatoires et dimensions, In: Recent progress in Fourier analysis (El Escorial, 1983), 65-121, North-Holland, Amsterdam (1985b). MR0848143 (87k:60110)
    • (1985) Ensembles Aléatoires et Dimensions
  • 13
    • 0039626381 scopus 로고
    • Ensembles parfaits et processus de lévy
    • MR0329050 (48:7392)
    • Ensembles parfaits et processus de Lévy, Period. Math. Hungar. 2 (1972), 49-59. MR0329050 (48:7392)
    • (1972) Period. Math. Hungar. , vol.2 , pp. 49-59
  • 14
    • 77950959109 scopus 로고
    • On the sum of two brownian paths
    • MR0554540 (80k:60100)
    • Robert Kaufman, On the sum of two Brownian paths, Studia. Math. LXV (1979), 51-54. MR0554540 (80k:60100)
    • (1979) Studia. Math. , vol.65 , pp. 51-54
    • Kaufman, R.1
  • 15
    • 33751397281 scopus 로고
    • Fourier analysis and paths of brownian motion
    • MR0397905 (53:1760)
    • Fourier analysis and paths of Brownian motion, Bull. Soc. Math. France 103 (1975), 427-432. MR0397905 (53:1760)
    • (1975) Bull. Soc. Math. France , vol.103 , pp. 427-432
  • 17
    • 22644448542 scopus 로고    scopus 로고
    • Brownian sheet images and bessel-Riesz capacity
    • MR1638246 (2000e:60123)
    • Brownian sheet images and Bessel-Riesz capacity, Trans. Amer. Math. Soc. 351(7) (1999), 2607-2622. MR1638246 (2000e:60123)
    • (1999) Trans. Amer. Math. Soc. , vol.351 , Issue.7 , pp. 2607-2622
  • 18
    • 18844399154 scopus 로고    scopus 로고
    • Lévy processes: Capacity and Hausdorff dimension
    • DOI 10.1214/009117904000001026
    • Davar Khoshnevisan and Yimin Xiao, Lévy Processes: Capacity and Hausdorff dimension, Ann. Probab. 33(3) (2005), 841-878. MR2135306 (2006d:60078) (Pubitemid 40689269)
    • (2005) Annals of Probability , vol.33 , Issue.3 , pp. 841-878
    • Khoshnevisan, D.1    Xiao, Y.2
  • 19
    • 84963036818 scopus 로고
    • A relation between dausdorff dimension and a condition on time sets for the image by the Brownian sheet to possess interior-points
    • MR0976063 (89m:60094)
    • T. S. Mountford, A relation between Hausdorff dimension and a condition on time sets for the image by the Brownian sheet to possess interior-points, Bull. London Math. Soc. 21 (1989), 179-185. MR0976063 (89m:60094)
    • (1989) Bull. London Math. Soc. , vol.21 , pp. 179-185
    • Mountford, T.S.1
  • 20
    • 77950945216 scopus 로고
    • An extension of a result of kahane using brownian local times of intersection
    • MR0943815 (89m:60197)
    • An extension of a result of Kahane using Brownian local times of intersection, Stochastics 23(4) (1988), 449-464. MR0943815 (89m:60197)
    • (1988) Stochastics , vol.23 , Issue.4 , pp. 449-464
  • 21
    • 0000498664 scopus 로고    scopus 로고
    • Lectures on probability theory and statistics (Saint-Flour, 1997) MR1746302 (2001c:60139)
    • Yuval Peres, Probability on Trees: An Introductory Climb, Lectures on probability theory and statistics (Saint-Flour, 1997), 1999, pp. 193-280. MR1746302 (2001c:60139)
    • (1999) Probability on Trees: An Introductory Climb , pp. 193-280
    • Peres, Y.1
  • 22
    • 0001564922 scopus 로고
    • Local times for gaussian vector fields
    • MR0471055 (57:10796)
    • Lauren D. Pitt, Local times for Gaussian vector fields, Indiana Univ. Math. J. 27 (1978), 309-330. MR0471055 (57:10796)
    • (1978) Indiana Univ. Math. J. , vol.27 , pp. 309-330
    • Pitt, L.D.1
  • 23
    • 0004160647 scopus 로고
    • Translated from the second Russian edition by Arlen Brown, Gordon and Breach Science Publishers, Inc., New York, MR0201557 (34:1439)
    • L. S. Pontryagin, Topological Groups, Translated from the second Russian edition by Arlen Brown, Gordon and Breach Science Publishers, Inc., New York, 1966. MR0201557 (34:1439)
    • (1966) Topological Groups
    • Pontryagin, L.S.1
  • 24
    • 35548946501 scopus 로고
    • Local time and a particle picture for euclidean field theory
    • MR0518340 (80a:81082)
    • Robert L. Wolpert, Local time and a particle picture for Euclidean field theory, J. Funct. Anal. 30(3) (1978), 341-357. MR0518340 (80a:81082)
    • (1978) J. Funct. Anal. , vol.30 , Issue.3 , pp. 341-357
    • Wolpert, R.L.1
  • 25
    • 0031231764 scopus 로고    scopus 로고
    • Hoelder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
    • DOI 10.1007/s004400050128
    • Yimin Xiao, Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields, Probab. Theory Rel. Fields 109 (1997), 129-157. MR1469923 (98m:60060) (Pubitemid 127127830)
    • (1997) Probability Theory and Related Fields , vol.109 , Issue.1 , pp. 129-157
    • Xiao, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.