Open Access
Volume 24, 2020
Page(s) 252 - 274
Published online 23 April 2020
  1. R.J. Adler and J.E. Taylor, Random fields and geometry. Springer Monographs in Mathematics. Springer, New York (2007). [Google Scholar]
  2. R.J. Adler and J.E. Taylor, Topological complexity of smooth random functions. Lectures from the 39th Probability Summer School held in Saint-Flour, 2009, École d’Été de Probabilités de Saint-Flour. [Saint-Flour Probability Summer School]. Vol. 2019 of Lecture Notes in Mathematics. Springer, Heidelberg (2011). [CrossRef] [Google Scholar]
  3. R.J. Adler, G. Samorodnitsky and J.E. Taylor, Excursion sets of three classes of stable random fields. Adv. Appl. Prob. 42 (2010) 293–318. [CrossRef] [Google Scholar]
  4. D. Beliaev, M. McAuley and S. Muirhead, On the number of excursion sets of planar Gaussian fields. Preprint to 1807.10209 (2018). [Google Scholar]
  5. C. Berzin, Estimation of Local Anisotropy Based on Level Sets. Preprint to 1801.03760 (2018). [Google Scholar]
  6. T.H. Beuman, A.M. Turner and V. Vitelli, Stochastic geometry and topology of non-Gaussian fields. Proc. Natl. Acad. Sci. 109 (2012) 19943–19948. [CrossRef] [Google Scholar]
  7. H. Biermé and A. Desolneux, On the perimeter of excursion sets of shot noise random fields. Ann. Probab. 44 (2016) 521–543. [Google Scholar]
  8. H. Biermé, E. Di Bernardino, C. Duval and A. Estrade, Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields. Electr. J. Stat. 13 (2019) 536–581. [CrossRef] [Google Scholar]
  9. F. Bron and D. Jeulin, Modelling a food microstructure by random sets. Image Anal. Stereol. 23 (2011). [Google Scholar]
  10. A. Bulinski, E. Spodarev and F. Timmermann, Central limit theorems for the excursion set volumes of weakly dependent random fields. Bernoulli 18 (2012) 100–118. [CrossRef] [Google Scholar]
  11. A.E. Burgess, Mammographic structure: Data preparation and spatial statistics analysis. Medical Imaging’99. International Society for Optics and Photonics (1999) 642–653. [Google Scholar]
  12. E.M. Cabaña, Affine processes: a test of isotropy based on level sets. SIAM J. Appl. Math. 47 (1987) 886–891. [Google Scholar]
  13. B. Casaponsa, B. Crill, L. Colombo, L. Danese, J. Bock, A. Catalano, A. Bonaldi, S. Basak, L. Bonavera, A. Coulais et al., Planck 2015 results: XVI. Isotropy and statistics of the CMB. Astron. Astrophys. 594 (2016) A16. [Google Scholar]
  14. E. Di Bernardino and C. Duval, Statistics for Gaussian Random Fields with Unknown Location and Scale using Lipschitz-Killing Curvatures. Preprint hal-02317747 (2019). [Google Scholar]
  15. A. Estrade and J.R. León, A central limit theorem for the Euler characteristic of a Gaussian excursion set. Ann. Probab. 44 (2016) 3849–3878. [Google Scholar]
  16. Y. Fantaye, D. Marinucci, F. Hansen and D. Maino, Applications of the Gaussian kinematic formula to CMB data analysis. Phys. Rev. D 91 (2015) 063501. [Google Scholar]
  17. M.Y. Hassan and R.H. Hijazi, A bimodal exponential power distribution. Pak. J. Stat. 26 (2010) 379–396. [Google Scholar]
  18. C. Hikage and T. Matsubara, Limits on second-order non-gaussianity from Minkowski functionals of WMAP data. Mon. Not. R. Astron. Soc. 425 (2012) 2187–2196. [Google Scholar]
  19. E. Hille, A class of reciprocal functions. Ann. Math. 27 (1926) 427–464. [Google Scholar]
  20. P. Imkeller, V. Pérez-Abreu and J. Vives, Chaos expansions of double intersection local time of Brownian motion in Rd and renormalization. Stoch. Process. Appl. 56 (1995) 1–34. [CrossRef] [Google Scholar]
  21. M. Kratz and J. León, Level curves crossings and applications for Gaussian models. Extremes 13 (2010) 315–351. [Google Scholar]
  22. M. Kratz and S. Vadlamani, Central limit theorem for Lipschitz–Killing curvatures of excursion sets of Gaussian random fields. J. Theor.Probab. 31 (2018) 1729–1758. [CrossRef] [Google Scholar]
  23. R. Lachièze-Rey, Normal convergence of nonlocalised geometric functionals and shot-noise excursions. Ann. Appl. Probab. 29 (2019) 2613–2653. [Google Scholar]
  24. D. Marinucci and G. Peccati, Random fields on the sphere. Representation, limit theorems and cosmological applications. In Vol. 389 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge (2011). [Google Scholar]
  25. D. Marinucci and M. Rossi, Stein-Malliavin approximations for nonlinear functionals of random eigenfunctions on 𝕊d. J. Funct. Anal. 268 (2015) 2379–2420. [Google Scholar]
  26. T. Matsubara, Analytic minkowski functionals of the cosmic microwave background: second-order non-gaussianity with bispectrum and trispectrum. Phys. Rev. D 81 (2010) 083505. [Google Scholar]
  27. D. Müller, A central limit theorem for Lipschitz–Killing curvatures of Gaussian excursions. J. Math. Anal. Appl. 452 (2017) 1040–1081. [Google Scholar]
  28. V.-H. Pham, On the rate of convergence for central limit theorems of sojourn times of Gaussian fields. Stoch. Process. Appl. 123 (2013) 2158–2174. [CrossRef] [Google Scholar]
  29. A. Roberts and M. Teubner, Transport properties of heterogeneous materials derived from Gaussian random fields: bounds and simulation. Phys. Rev. E 51 (1995) 4141–4154. [Google Scholar]
  30. A. Roberts and S. Torquato, Chord-distribution functions of three-dimensional random media: approximate first-passage times of Gaussian processes. Phys. Rev. E 59 (1999) 4953–4963. [Google Scholar]
  31. R. Schneider and W. Weil, Stochastic and integral geometry. Probability and its Applications. Springer-Verlag, Berlin (2008). [CrossRef] [Google Scholar]
  32. E. Spodarev, Limit theorems for excursion sets of stationary random fields. In Modern stochastics and applications, vol. 90 of Springer Optim. Appl. Springer, Cham (2014) 221–241. [Google Scholar]
  33. C. Thäle, 50 years sets with positive reach – a survey. Surv. Math. Appl. 3 (2008) 123–165. [Google Scholar]
  34. K.J. Worsley, The geometry of random images. Chance 1 (1997) 27–40. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.