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Volumn 63, Issue , 2011, Pages 279-308

Properties of Strong Local Nondeterminism and Local Times of Stable Random Fields

Author keywords

harmonizable fractional stable motion; harmonizable fractional stable sheets; H lder condition; joint continuity; linear fractional stable sheets; local times; Stable random fields; strong local nondeterminism

Indexed keywords


EID: 85145050303     PISSN: 10506977     EISSN: 22970428     Source Type: Book Series    
DOI: 10.1007/978-3-0348-0021-1_18     Document Type: Chapter
Times cited : (18)

References (46)
  • 3
    • 33947262690 scopus 로고    scopus 로고
    • Local and asymptotic properties of linear fractional stable sheets
    • A. Ayache, F. Roueff, and Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C. R. Acad. Sci. Paris, Ser. A., 344 (2007), 389–394.
    • (2007) C. R. Acad. Sci. Paris, Ser. A , vol.344 , pp. 389-394
    • Ayache, A.1    Roueff, F.2    Xiao, Y.3
  • 4
    • 34249016402 scopus 로고    scopus 로고
    • Joint continuity of the local times of linear fractional stable sheets
    • A. Ayache, F. Roueff, and Y. Xiao, Joint continuity of the local times of linear fractional stable sheets, C. R. Acad. Sci. Paris, Ser. A., 344 (2007), 635–640.
    • (2007) C. R. Acad. Sci. Paris, Ser. A , vol.344 , pp. 635-640
    • Ayache, A.1    Roueff, F.2    Xiao, Y.3
  • 5
    • 61849122957 scopus 로고    scopus 로고
    • Linear fractional stable sheets: wavelet expansion and sample path properties
    • A. Ayache, F. Roueff, and Y. Xiao, Linear fractional stable sheets: wavelet expansion and sample path properties, Stoch. Process. Appl., 119 (2009), 1168–1197.
    • (2009) Stoch. Process. Appl , vol.119 , pp. 1168-1197
    • Ayache, A.1    Roueff, F.2    Xiao, Y.3
  • 7
    • 53349150315 scopus 로고    scopus 로고
    • Joint continuity of the local times of fractional Brownian sheets
    • A. Ayache, D. Wu, and Y. Xiao, Joint continuity of the local times of fractional Brownian sheets, Ann. Inst. H. Poincaré Probab. Statist., 44 (2008), 727–748.
    • (2008) Ann. Inst. H. Poincaré Probab. Statist , vol.44 , pp. 727-748
    • Ayache, A.1    Wu, D.2    Xiao, Y.3
  • 8
    • 23944466359 scopus 로고    scopus 로고
    • Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets
    • A. Ayache and Y. Xiao, Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, J. Fourier Anal. Appl., 11 (2005), 407–439.
    • (2005) J. Fourier Anal. Appl , vol.11 , pp. 407-439
    • Ayache, A.1    Xiao, Y.2
  • 9
    • 0002807832 scopus 로고
    • Local nondeterminism and local times of Gaussian processes
    • S.M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J., 23 (1973), 69–94.
    • (1973) Indiana Univ. Math. J , vol.23 , pp. 69-94
    • Berman, S.M.1
  • 12
    • 0010881976 scopus 로고
    • On moduli of continuity for local times of Gaussian processes
    • M. Csörgő, Z.-Y. Lin, and Q.-M. Shao, On moduli of continuity for local times of Gaussian processes, Stoch. Process. Appl., 58 (1995), 1–21.
    • (1995) Stoch. Process. Appl , vol.58 , pp. 1-21
    • Csörgő, M.1    Lin, Z.-Y.2    Shao, Q.-M.3
  • 14
    • 0031575042 scopus 로고    scopus 로고
    • Local time for stable moving average processes: Hölder conditions
    • M. Dozzi and A.R. Soltani, Local time for stable moving average processes: Hölder conditions, Stoch. Process. Appl., 68 (1997), 195–207.
    • (1997) Stoch. Process. Appl , vol.68 , pp. 195-207
    • Dozzi, M.1    Soltani, A.R.2
  • 15
    • 0001287276 scopus 로고
    • Sample function properties of multi-parameter stable processes
    • W. Ehm, Sample function properties of multi-parameter stable processes, Z. Wahrsch. verw. Gebiete, 56 (1981), 195–228.
    • (1981) Z. Wahrsch. verw. Gebiete , vol.56 , pp. 195-228
    • Ehm, W.1
  • 16
    • 0002902384 scopus 로고
    • Occupation densities
    • D. Geman and J. Horowitz, Occupation densities, Ann. Probab., 8 (1980), 1–67.
    • (1980) Ann. Probab , vol.8 , pp. 1-67
    • Geman, D.1    Horowitz, J.2
  • 19
    • 33748947145 scopus 로고    scopus 로고
    • Sectorial local nondeterminism and the geometry of the Brownian sheet
    • D. Khoshnevisan, D. Wu, and Y. Xiao, Sectorial local nondeterminism and the geometry of the Brownian sheet, Electron. J. Probab., 11 (2006), 817–843.
    • (2006) Electron. J. Probab , vol.11 , pp. 817-843
    • Khoshnevisan, D.1    Wu, D.2    Xiao, Y.3
  • 21
    • 0039039367 scopus 로고
    • Local times and related sample path properties of certain self-similar processes
    • N. Kôno and N.-R. Shieh, Local times and related sample path properties of certain self-similar processes, J. Math. Kyoto Univ., 33 (1993), 51–64.
    • (1993) J. Math. Kyoto Univ , vol.33 , pp. 51-64
    • Kôno, N.1    Shieh, N.-R.2
  • 23
    • 33749620020 scopus 로고    scopus 로고
    • Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards
    • J.B. Levy and M.S. Taqqu, Renewal reward processes with heavy-tailed interrenewal times and heavy-tailed rewards, Bernoulli, 6 (2000), 23–44.
    • (2000) Bernoulli , vol.6 , pp. 23-44
    • Levy, J.B.1    Taqqu, M.S.2
  • 24
    • 0004148844 scopus 로고    scopus 로고
    • American Mathematical Society, Rhode Island
    • E.H. Lieb and M. Loss, Analysis, American Mathematical Society, Rhode Island, 1997.
    • (1997) Analysis
    • Lieb, E.H.1    Loss, M.2
  • 25
    • 0041042279 scopus 로고
    • A self-similar process with nowhere bounded sample paths
    • M. Maejima, A self-similar process with nowhere bounded sample paths, Z. Wahrsch. Verw. Gebiete, 65 (1983), 115–119.
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.65 , pp. 115-119
    • Maejima, M.1
  • 27
    • 0000746459 scopus 로고
    • Path properties of index-β stable fields
    • J.P. Nolan, Path properties of index-β stable fields, Ann. Probab., 16 (1988), 1596– 1607.
    • (1988) Ann. Probab , vol.16 , pp. 1596-1607
    • Nolan, J.P.1
  • 28
    • 0001345881 scopus 로고
    • Local nondeterminism and local times for stable processes
    • J.P. Nolan, Local nondeterminism and local times for stable processes, Probab. Th. Rel. Fields, 82 (1989), 387–410.
    • (1989) Probab. Th. Rel. Fields , vol.82 , pp. 387-410
    • Nolan, J.P.1
  • 30
    • 0001646544 scopus 로고    scopus 로고
    • The limit of a renewal-reward process with heavy-tailed rewards is not a linear fractional stable motion
    • V. Pipiras and M.S. Taqqu, The limit of a renewal-reward process with heavy-tailed rewards is not a linear fractional stable motion, Bernoulli, 6 (2000), 607–614.
    • (2000) Bernoulli , vol.6 , pp. 607-614
    • Pipiras, V.1    Taqqu, M.S.2
  • 31
    • 84959668466 scopus 로고
    • On the behavior of the characteristic function of a probability distribution in the neighbourhood of the origin
    • E.J.G. Pitman, On the behavior of the characteristic function of a probability distribution in the neighbourhood of the origin, J. Australian Math. Soc. Series A, 8 (1968), 422–443.
    • (1968) J. Australian Math. Soc. Series A , vol.8 , pp. 422-443
    • Pitman, E.J.G.1
  • 32
    • 0001564922 scopus 로고
    • Local times for Gaussian vector fields
    • L.D. Pitt, Local times for Gaussian vector fields, Indiana Univ. Math. J., 27 (1978), 309–330.
    • (1978) Indiana Univ. Math. J , vol.27 , pp. 309-330
    • Pitt, L.D.1
  • 35
    • 70350706443 scopus 로고
    • Multiple points of fractional stable processes
    • N.-R. Shieh, Multiple points of fractional stable processes, J. Math. Kyoto Univ., 33 (1993), 731–741.
    • (1993) J. Math. Kyoto Univ , vol.33 , pp. 731-741
    • Shieh, N.-R.1
  • 37
    • 84972567300 scopus 로고
    • Sample path properties of ergodic self-similar processes
    • K. Takashima, Sample path properties of ergodic self-similar processes, Osaka J. Math., 26 (1989), 159–189.
    • (1989) Osaka J. Math , vol.26 , pp. 159-189
    • Takashima, K.1
  • 38
    • 33846996313 scopus 로고    scopus 로고
    • Geometric properties of the images of fractional Brownian sheets
    • D. Wu and Y. Xiao, Geometric properties of the images of fractional Brownian sheets, J. Fourier Anal. Appl., 13 (2007), 1–37.
    • (2007) J. Fourier Anal. Appl , vol.13 , pp. 1-37
    • Wu, D.1    Xiao, Y.2
  • 39
    • 64549090713 scopus 로고    scopus 로고
    • Continuity with respect to the Hurst index of the local times of anisotropic Gaussian random fields
    • D. Wu and Y. Xiao, Continuity with respect to the Hurst index of the local times of anisotropic Gaussian random fields, Stoch. Process. Appl., 119 (2009), 1823–1844.
    • (2009) Stoch. Process. Appl , vol.119 , pp. 1823-1844
    • Wu, D.1    Xiao, Y.2
  • 40
    • 0001025635 scopus 로고
    • Dimension results for Gaussian vector fields and index-α stable fields
    • Y. Xiao, Dimension results for Gaussian vector fields and index-α stable fields, Ann. Probab., 23 (1995), 273–291.
    • (1995) Ann. Probab , vol.23 , pp. 273-291
    • Xiao, Y.1
  • 41
    • 0031231764 scopus 로고    scopus 로고
    • Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
    • Y. Xiao, Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields, Probab. Theory Relat. Fields, 109 (1997), 129–157.
    • (1997) Probab. Theory Relat. Fields , vol.109 , pp. 129-157
    • Xiao, Y.1
  • 42
    • 33846986040 scopus 로고    scopus 로고
    • Properties of local nondeterminism of Gaussian and stable random fields and their applications
    • Y. Xiao, Properties of local nondeterminism of Gaussian and stable random fields and their applications, Ann. Fac. Sci. Toulouse Math., XV (2006), 157–193.
    • (2006) Ann. Fac. Sci. Toulouse Math , vol.XV , pp. 157-193
    • Xiao, Y.1
  • 43
    • 47249119021 scopus 로고    scopus 로고
    • Strong local nondeterminism and sample path properties of Gaussian random fields
    • Tze Leung Lai, Qiman Shao, Lianfen Qian, Eds., Higher Education Press
    • Y. Xiao, Strong local nondeterminism and sample path properties of Gaussian random fields, In: Asymptotic Theory in Probability and Statistics with Applications, Tze Leung Lai, Qiman Shao, Lianfen Qian, Eds., Higher Education Press, 2007, 136–176.
    • (2007) Asymptotic Theory in Probability and Statistics with Applications , pp. 136-176
    • Xiao, Y.1
  • 44
    • 54049120647 scopus 로고    scopus 로고
    • Sample path properties of anisotropic Gaussian random fields
    • D. Khoshnevisan and F. Rassoul-Agha, Eds., Lect. Notes in Math., (2009), Springer, New York
    • Y. Xiao, Sample path properties of anisotropic Gaussian random fields, In: A Mini-course on Stochastic Partial Differential Equations, D. Khoshnevisan and F. Rassoul-Agha, Eds., Lect. Notes in Math., 1962 (2009), 145–212, Springer, New York.
    • A Mini-course on Stochastic Partial Differential Equations , vol.1962 , pp. 145-212
    • Xiao, Y.1
  • 45
    • 70450233652 scopus 로고    scopus 로고
    • On uniform modulus of continuity of random fields
    • Y. Xiao, On uniform modulus of continuity of random fields, Monatsh. Math., DOI 10.1007/s00605-009-0133-z, 2009.
    • (2009) Monatsh. Math
    • Xiao, Y.1
  • 46
    • 0035981340 scopus 로고    scopus 로고
    • Local times of fractional Brownian sheets
    • Y. Xiao and T. Zhang, Local times of fractional Brownian sheets, Probab. Theory Relat. Fields, 124 (2002), 204–226.
    • (2002) Probab. Theory Relat. Fields , vol.124 , pp. 204-226
    • Xiao, Y.1    Zhang, T.2


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