A multiparameter Garsia–Rodemich–Rumsey inequality and some applications
Tài liệu tham khảo
Ayache, 2002, Drap brownien fractionnaire, Potential Anal., 17, 31, 10.1023/A:1015260803576
Ayache, 2005, Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, J. Fourier Anal. Appl., 11, 407, 10.1007/s00041-005-4048-3
Fernique, 1964, Continuité des processus Gaussiens, C. R. Acad. Sci. Paris, 258, 6058
Fernique, 1966, Séries de distributions aléatoires indépendantes, C. R. Acad. Sci. Paris Sér. A–B, 263, A674
X. Fernique, Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens. Université de Montréal, Centre de Recherches Mathématiques, Montreal, QC, 1997.
Garsia, 1970, A real variable lemma and the continuity of paths of some Gaussian processes, Indiana Univ. Math. J., 20, 565, 10.1512/iumj.1971.20.20046
Marcus, 1970, Continuity of Gaussian processes, Trans. Amer. Math. Soc., 151, 377, 10.1090/S0002-9947-1970-0264749-1
Meerschaert, 2013, Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields, Trans. Amer. Math. Soc., 365, 1081, 10.1090/S0002-9947-2012-05678-9
Orey, 1973, Sample functions of the N-parameter Wiener process, Ann. Probab., 1, 138, 10.1214/aop/1176997030
Ral’chenko, 2007, The two-parameter Garsia–Rodemich–Rumsey inequality and its application to fractional Brownian fields, Theory Probab. Math. Statist., 75, 167, 10.1090/S0094-9000-08-00723-0
Xiao, 2009, Sample path properties of anisotropic Gaussian random fields. A minicourse on stochastic partial differential equations, vol. 1962, 145
Zimmerman, 1972, Some sample function properties of the two-parameter Gaussian process, Ann. Math. Statist., 43, 1235, 10.1214/aoms/1177692475