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Volumn 34, Issue 1, 2006, Pages 122-158

A Gaussian kinematic formula

Author keywords

Euler characteristic; Excursions; Gaussian processes; Manifolds; Random fields; Riemannian geometry

Indexed keywords


EID: 33644944828     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117905000000594     Document Type: Article
Times cited : (66)

References (24)
  • 2
    • 0034392041 scopus 로고    scopus 로고
    • On excursion sets, tube formulae, and maxima of random fields
    • MR1765203
    • ADLER, R. J. (2000). On excursion sets, tube formulae, and maxima of random fields. Ann. Appl. Probab. 10 1-74. MR1765203
    • (2000) Ann. Appl. Probab. , vol.10 , pp. 1-74
    • Adler, R.J.1
  • 3
    • 33845295405 scopus 로고    scopus 로고
    • Birkhäuser, Boston. To appear. Preliminary versions of Chapters 1-12
    • ADLER, R. J. and TAYLOR, J. E. (2006). Random Fields and Geometry. Birkhäuser, Boston. To appear. Preliminary versions of Chapters 1-12 available at http://iew3.technion.ac.il/~radler/grf.pdf.
    • (2006) Random Fields and Geometry
    • Adler, R.J.1    Taylor, J.E.2
  • 4
    • 0000192391 scopus 로고
    • Differential calculus on finite codimensional submanifolds of the Wiener space - The divergence operator
    • MR1125228
    • AIRAULT, H. (1991). Differential calculus on finite codimensional submanifolds of the Wiener space - the divergence operator. J. Funct. Anal. 100 291-316. MR1125228
    • (1991) J. Funct. Anal. , vol.100 , pp. 291-316
    • Airault, H.1
  • 5
    • 0002535640 scopus 로고
    • Intégration géométrique sur l'espace de Wiener
    • MR942797
    • AIRAULT, H. and MALLIAVIN, P. (1988). Intégration géométrique sur l'espace de Wiener. Bull. Sci. Math. (2) 112 3-52. MR942797
    • (1988) Bull. Sci. Math. (2) , vol.112 , pp. 3-52
    • Airault, H.1    Malliavin, P.2
  • 7
    • 0036433746 scopus 로고    scopus 로고
    • Lipschitz-Killing invariants
    • MR1936341
    • BERNIG, A. and BRÖCKER, L. (2002). Lipschitz-Killing invariants. Math. Nachr. 245 5-25. MR1936341
    • (2002) Math. Nachr. , vol.245 , pp. 5-25
    • Bernig, A.1    Bröcker, L.2
  • 9
    • 0001036635 scopus 로고
    • A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
    • MR11027
    • CHERN, S.-S. (1944). A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds. Ann. of Math. (2) 45 747-752. MR11027
    • (1944) Ann. of Math. (2) , vol.45 , pp. 747-752
    • Chern, S.-S.1
  • 10
    • 0007288995 scopus 로고
    • On the kinematic formula in integral geometry
    • MR198406
    • CHERN, S.-S. (1966). On the kinematic formula in integral geometry. J. Math. Mech. 16 101-118. MR198406
    • (1966) J. Math. Mech. , vol.16 , pp. 101-118
    • Chern, S.-S.1
  • 11
    • 84968469617 scopus 로고
    • Curvature measures
    • MR110078
    • FEDERER, H. (1959). Curvature measures. Trans. Amer. Math. Soc. 93418-491. MR110078
    • (1959) Trans. Amer. Math. Soc. , vol.93 , pp. 418-491
    • Federer, H.1
  • 12
    • 0004203250 scopus 로고
    • Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA. MR1044996
    • GRAY, A. (1990). Tubes. Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA. MR1044996
    • (1990) Tubes
    • Gray, A.1
  • 15
    • 0004454158 scopus 로고
    • Testing for a signal with unknown location and scale in a stationary Gaussian random field
    • MR1332585
    • SIEGMUND, D. O. and WORSLEY, K. J. (1995). Testing for a signal with unknown location and scale in a stationary Gaussian random field. Ann. Statist. 23 608-639. MR1332585
    • (1995) Ann. Statist. , vol.23 , pp. 608-639
    • Siegmund, D.O.1    Worsley, K.J.2
  • 16
    • 0036331007 scopus 로고    scopus 로고
    • Maximum of Gaussian field on piecewise smooth domain: Equivalence of tube method and Euler characteristic method
    • MR1910648
    • TAKEMURA, A. and KURIKI, S. (2002). Maximum of Gaussian field on piecewise smooth domain: Equivalence of tube method and Euler characteristic method. Ann. Appl. Probab. 12 768-796. MR1910648
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 768-796
    • Takemura, A.1    Kuriki, S.2
  • 17
    • 23244455084 scopus 로고    scopus 로고
    • Validity of the expected Euler characteristic heuristic
    • MR2150192
    • TAYLOR, J., TAKEMURA, A. and ADLER, R. (2005). Validity of the expected Euler characteristic heuristic. Ann. Probab. 33 1362-1396. MR2150192
    • (2005) Ann. Probab. , vol.33 , pp. 1362-1396
    • Taylor, J.1    Takemura, A.2    Adler, R.3
  • 18
    • 0038336161 scopus 로고    scopus 로고
    • Euler characteristics for Gaussian fields on manifolds
    • MR1964940
    • TAYLOR, J. E. and ADLER, R. J. (2003). Euler characteristics for Gaussian fields on manifolds. Ann. Probab. 31 533-563. MR1964940
    • (2003) Ann. Probab. , vol.31 , pp. 533-563
    • Taylor, J.E.1    Adler, R.J.2
  • 19
    • 0000045032 scopus 로고
    • On the volume of tubes
    • MR1507388
    • WEYL, H. (1939). On the volume of tubes. Amer. J. Math. 61461-472. MR1507388
    • (1939) Amer. J. Math. , vol.61 , pp. 461-472
    • Weyl, H.1
  • 21
    • 0001464776 scopus 로고
    • Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics
    • MR1358902
    • WORSLEY, K. J. (1995). Boundary corrections for the expected Euler characteristic of excursion sets of random fields, with an application to astrophysics. Adv. in Appl. Probab. 27 943-959. MR1358902
    • (1995) Adv. in Appl. Probab. , vol.27 , pp. 943-959
    • Worsley, K.J.1
  • 22
    • 21844486695 scopus 로고
    • Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images
    • MR1332586
    • WORSLEY, K. J. (1995). Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images. Ann. Statist. 23640-669. MR1332586
    • (1995) Ann. Statist. , vol.23 , pp. 640-669
    • Worsley, K.J.1
  • 23
    • 0002087618 scopus 로고    scopus 로고
    • The geometry of random images
    • WORSLEY, K. J. (1996). The geometry of random images. Chance 9 27-40.
    • (1996) Chance , vol.9 , pp. 27-40
    • Worsley, K.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.