Project Euclid

References

• [1] Anh, V.V. and Leonenko, N.N. (1999). Non-Gaussian scenarios for the heat equation with singular initial conditions. Stochastic Process. Appl. 84 91–114.
  Zentralblatt MATH: 1001.60071
  Digital Object Identifier: doi:10.1016/S0304-4149(99)00053-8
  
• [2] Anh, V.V., Leonenko, N.N. and Ruiz-Medina, M.D. (2013). Macroscaling limit theorems for filtered spatiotemporal random fields. Stoch. Anal. Appl. 31 460–508.
  Zentralblatt MATH: 1327.62095
  Digital Object Identifier: doi:10.1080/07362994.2013.777280
  
• [3] Applebaum, D. (2004). Lévy Processes and Stochastic Calculus. Cambridge Studies in Advanced Mathematics 93. Cambridge: Cambridge Univ. Press.
• [4] Bateman, H. and Erdelyi, A. (1953). Higher Transcenental Functions II. New York: McGraw-Hill.
• [5] Berman, S.M. (1982). Local times of stochastic processes with positive definite bivariate densities. Stochastic Process. Appl. 12 1–26.
  Zentralblatt MATH: 0471.60082
  Digital Object Identifier: doi:10.1016/0304-4149(81)90009-0
  
• [6] Berman, S.M. (1984). Sojourns of vector Gaussian processes inside and outside spheres. Z. Wahrsch. Verw. Gebiete 66 529–542.
  Zentralblatt MATH: 0561.60042
  Digital Object Identifier: doi:10.1007/BF00531889
  
• [7] Brelot, M. (1960). Lectures on Potential Theory. Notes by K. N. Gowrisankaran and M. K. Venkatesha Murthy. Lectures on Mathematics 19. Bombay: Tata Institute of Fundamental Research.
• [8] Bulinski, A., Spodarev, E. and Timmermann, F. (2012). Central limit theorems for the excursion set volumes of weakly dependent random fields. Bernoulli 18 100–118.
  Zentralblatt MATH: 1239.60017
  Digital Object Identifier: doi:10.3150/10-BEJ339
  Project Euclid: euclid.bj/1327068619
  
• [9] Caetano, A.M. (2000). Approximation by functions of compact support in Besov–Triebel–Lizorkin spaces on irregular domains. Studia Math. 142 47–63.
• [10] Chen, Z.-Q., Meerschaert, M.M. and Nane, E. (2012). Space–time fractional diffusion on bounded domains. J. Math. Anal. Appl. 393 479–488.
  Zentralblatt MATH: 1251.35177
  Digital Object Identifier: doi:10.1016/j.jmaa.2012.04.032
  
• [11] Dautray, R. and Lions, J.-L. (1990). Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 3. Berlin: Springer.
  Zentralblatt MATH: 0683.35001
  
• [12] Dobrushin, R.L. and Major, P. (1979). Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 27–52.
  Zentralblatt MATH: 0397.60034
  Digital Object Identifier: doi:10.1007/BF00535673
  
• [13] Doukhan, P., León, J.R. and Soulier, P. (1996). Central and non-central limit theorems for quadratic forms of a strongly dependent Gaussian field. Rebrape 10 205–223.
  Zentralblatt MATH: 0881.60023
  
• [14] Engliš, M. and Ali, S.T. (2015). Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics. J. Math. Phys. 56 072109, 22.
• [15] Finlay, R. and Seneta, E. (2007). A gamma activity time process with noninteger parameter and self-similar limit. J. Appl. Probab. 44 950–959.
  Zentralblatt MATH: 1181.60053
  Digital Object Identifier: doi:10.1017/S002190020000365X
  
• [16] Fox, R. and Taqqu, M.S. (1985). Noncentral limit theorems for quadratic forms in random variables having long-range dependence. Ann. Probab. 13 428–446.
  Mathematical Reviews (MathSciNet): MR781415
  Zentralblatt MATH: 0569.60016
  Digital Object Identifier: doi:10.1214/aop/1176993001
  Project Euclid: euclid.aop/1176993001
  
• [17] Fuglede, B. (2005). Dirichlet problems for harmonic maps from regular domains. Proc. Lond. Math. Soc. (3) 91 249–272.
  Zentralblatt MATH: 1080.58015
  
• [18] Gajek, L. and Mielniczuk, J. (1999). Long- and short-range dependent sequences under exponential subordination. Statist. Probab. Lett. 43 113–121.
  Zentralblatt MATH: 0943.60013
  Digital Object Identifier: doi:10.1016/S0167-7152(98)00188-6
  
• [19] Heyde, C.C. and Leonenko, N.N. (2005). Student processes. Adv. in Appl. Probab. 37 342–365.
  Zentralblatt MATH: 1081.60035
  Digital Object Identifier: doi:10.1017/S0001867800000215
  
• [20] Joe, H. (1997). Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability 73. London: Chapman & Hall.
  Zentralblatt MATH: 0990.62517
  
• [21] Lancaster, H.O. (1958). The structure of bivariate distributions. Ann. Math. Stat. 29 719–736.
  Zentralblatt MATH: 0086.35102
  Digital Object Identifier: doi:10.1214/aoms/1177706532
  
• [22] Lancaster, H.O. (1963). Correlations and canonical forms of bivariate distributions. Ann. Math. Stat. 34 532–538.
  Zentralblatt MATH: 0115.14104
  Digital Object Identifier: doi:10.1214/aoms/1177704165
  
• [23] Leonenko, N. (1999). Limit Theorems for Random Fields with Singular Spectrum. Mathematics and Its Applications 465. Dordrecht: Kluwer Academic.
  Zentralblatt MATH: 0963.60048
  
• [24] Leonenko, N. and Olenko, A. (2014). Sojourn measures of Student and Fisher–Snedecor random fields. Bernoulli 20 1454–1483.
  Mathematical Reviews (MathSciNet): MR3217450
  Zentralblatt MATH: 1304.60058
  Digital Object Identifier: doi:10.3150/13-BEJ529
  Project Euclid: euclid.bj/1402488946
  
• [25] Leonenko, N.N., Meerschaert, M.M. and Sikorskii, A. (2013). Fractional Pearson diffusions. J. Math. Anal. Appl. 403 532–546.
  Zentralblatt MATH: 1297.60057
  Digital Object Identifier: doi:10.1016/j.jmaa.2013.02.046
  
• [26] Leonenko, N.N., Ruiz-Medina, M.D. and Taqqu, M. (2015). Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence. Available at arXiv:1501.02247 [math.ST].
  arXiv: 1501.02247
  Zentralblatt MATH: 1359.60066
  Digital Object Identifier: doi:10.1080/07362994.2016.1230723
  
• [27] Lim, S.C. and Teo, L.P. (2010). Analytic and asymptotic properties of multivariate generalized Linnik’s probability densities. J. Fourier Anal. Appl. 16 715–747.
  Zentralblatt MATH: 1202.60028
  Digital Object Identifier: doi:10.1007/s00041-009-9097-6
  
• [28] Linde, A. and Mukhanov, V.F. (1997). Non-Gaussian isocurvature perturbations from inflation. Phys. Rev. D 56 535.
• [29] Lukacs, E. (1970). Characteristic Functions, 2nd ed. New York: Hafner Publishing.
  Zentralblatt MATH: 0201.20404
  
• [30] Major, P. (1981). Multiple Wiener–Itô Integrals: With Applications to Limit Theorems. Lecture Notes in Math. 849. Berlin: Springer.
• [31] Marinucci, D. and Peccati, G. (2011). Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications. London Mathematical Society Lecture Note Series 389. Cambridge: Cambridge Univ. Press.
  Zentralblatt MATH: 1260.60004
  
• [32] Mielniczuk, J. (2000). Some properties of random stationary sequences with bivariate densities having diagonal expansions and nonparametric estimators based on them. J. Nonparametr. Stat. 12 223–243.
  Mathematical Reviews (MathSciNet): MR1752314
  Zentralblatt MATH: 0944.62084
  Digital Object Identifier: doi:10.1080/10485250008832806
  
• [33] Novikov, D., Schmalzing, J. and Mukhanov, V.F. (2000). On non-Gaussianity in the cosmic microwave background. Astronom. Astrophys. Lib. 364 17–25.
• [34] Osswald, H. (2012). Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion: An Introduction. Cambridge Tracts in Mathematics 191. Cambridge: Cambridge Univ. Press.
  Zentralblatt MATH: 1264.60037
  
• [35] Rajput, B.S. and Rosiński, J. (1989). Spectral representations of infinitely divisible processes. Probab. Theory Related Fields 82 451–487.
• [36] Sarmanov, O.V. (1963). Investigation of stationary Markov processes by the method of eigenfunction expansion. Translated in Selected Translations in Mathematical Statistics and Probability Theory Amer. Math. Amer. Math. Soc., Providence 4 245–269.
  Zentralblatt MATH: 0275.60085
  
• [37] Simon, B. (2005). Trace Ideals and Their Applications, 2nd ed. Mathematical Surveys and Monographs 120. Providence, RI: Amer. Math. Soc.
  Zentralblatt MATH: 1074.47001
  
• [38] Stein, E.M. (1970). Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, No. 30. Princeton, NJ: Princeton Univ. Press.
  Zentralblatt MATH: 0207.13501
  
• [39] Taqqu, M.S. (1974/75). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 287–302.
• [40] Taqqu, M.S. (1979). Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrsch. Verw. Gebiete 50 53–83.
• [41] Taylor, J.E. and Worsley, K.J. (2007). Detecting sparse signals in random fields, with an application to brain mapping. J. Amer. Statist. Assoc. 102 913–928.
  Mathematical Reviews (MathSciNet): MR2354405
  Zentralblatt MATH: 05564420
  Digital Object Identifier: doi:10.1198/016214507000000815
  
• [42] Triebel, H. (1978). Interpolation Theory, Function Spaces, Differential Operators. North-Holland Mathematical Library 18. New York: North-Holland.
• [43] Veillette, M.S. and Taqqu, M.S. (2013). Properties and numerical evaluation of the Rosenblatt distribution. Bernoulli 19 982–1005.
  Zentralblatt MATH: 1273.60020
  Digital Object Identifier: doi:10.3150/12-BEJ421
  Project Euclid: euclid.bj/1372251150
  
• [44] Wong, E. and Thomas, J.B. (1962). On polynomial expansions of second-order distributions. J. Soc. Indust. Appl. Math. 10 507–516.
  Zentralblatt MATH: 0111.32806
  Digital Object Identifier: doi:10.1137/0110038
  
• [45] Worsley, K.J. (2001). Testing for signals with unknown location and scale in a $\chi^{2}$ random field, with an application to fMRI. Adv. in Appl. Probab. 33 773–793.
  Zentralblatt MATH: 0991.62075