A fractional Brownian field indexed byL2and a varying Hurst parameter

Stochastic Processes and their Applications - Tập 125 - Trang 1394-1425 - 2015
Alexandre Richard1
1Regularity team, INRIA Saclay and Laboratoire MAS, Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France

Tài liệu tham khảo

Adler, 2007 Ayache, 2005, Multifractional processes with random exponent, Publ. Mat., 49, 459, 10.5565/PUBLMAT_49205_11 Benassi, 1997, Elliptic Gaussian random processes, Rev. Mat. Iberoam., 13, 19, 10.4171/RMI/217 H. Biermé, O. Durieu, Invariance principles for self-similar set-indexed sums of dependent random fields, Preprint, 2012, pp. 1–22. Borell, 1976, Gaussian Radon measure on locally convex spaces, Math. Scand., 38, 265, 10.7146/math.scand.a-11634 R. Carmona, Tensor product of Gaussian measures, in: Conference on Vector Space Measures and Applications, Dublin, 1977, pp. 96–124. Dalang, 1999, Extending martingale measure stochastic integral with applications to spatially homogeneous S.P.D.E’s, Electron. J. Probab., 4, 1, 10.1214/EJP.v4-43 Decreusefond, 1999, Stochastic analysis of the fractional Brownian motion, Potential Anal., 411, 177, 10.1023/A:1008634027843 Dobric, 2006, Fractional Brownian fields, duality, and martingales, vol. 51, 77 Dudley, 1973, Sample functions of the Gaussian process, Ann. Probab., 1, 66, 10.1214/aop/1176997026 Fernique, 1975, Des résultats nouveaux sur les processus gaussiens, 318 Gel’fand, 1964 Gikhman, 1969 Goodman, 1988, Characteristics of normal samples, Ann. Probab., 16, 1281, 10.1214/aop/1176991690 Gross, 1967, Abstract Wiener spaces, 31 Herbin, 2006, From N parameter fractional Brownian motions to N parameter multifractional Brownian motions, Rocky Mountain J. Math., 36, 1249, 10.1216/rmjm/1181069415 Herbin, 2009, Stochastic 2-microlocal analysis, Stochastic Process. Appl., 119, 2277, 10.1016/j.spa.2008.11.005 Herbin, 2006, A set-indexed fractional Brownian motion, J. Theoret. Probab., 19, 337, 10.1007/s10959-006-0019-0 E. Herbin, A. Richard, Local Hölder regularity of set-indexed processes, Preprint, 2012, arXiv:1203.0750v1. E. Herbin, Y. Xiao, Sample paths properties of the set-indexed fractional Brownian motion (2014), in preparation. Ivanoff, 2000 Jolis, 2007, On the Wiener integral with respect to the fractional Brownian motion on an interval, J. Math. Anal. Appl., 330, 1115, 10.1016/j.jmaa.2006.07.100 Jolis, 2010, Continuity of the Hurst parameter of the law of the symmetric integral with respect to the fractional Brownian motion, Stochastic Process. Appl., 120, 1651, 10.1016/j.spa.2010.05.002 Khoshnevisan, 2002 Kuelbs, 1993, Metric entropy and the small ball problem for Gaussian measures, J. Funct. Anal., 116, 133, 10.1006/jfan.1993.1107 Kuo, 1975 Leonenko, 2011, Fractional elliptic, hyperbolic and parabolic random fields, Electron. J. Probab., 16, 1134, 10.1214/EJP.v16-891 Lévy, 1965 Marcus, 2006 Monrad, 1995, Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Theory Related Fields, 101, 173, 10.1007/BF01375823 Nualart, 2006 Nualart, 1995, Quasilinear stochastic elliptic equations with reflection, Stochastic Process. Appl., 57, 73, 10.1016/0304-4149(95)00006-S Peltier, 1995 Pitt, 1978, Local times for Gaussian vector fields, Indiana Univ. Math. J., 27, 309, 10.1512/iumj.1978.27.27024 Reed, 1980 Rudin, 1987 Ryan, 2002 Samorodnitsky, 1994 Schilling, 2012 Shao, 1995, Small ball probabilities of Gaussian fields, Probab. Theory Related Fields, 102, 511, 10.1007/BF01198847 Stroock, 2010 Takenaka, 1981, Brownian motion parametrized with metric space of constant curvature, Nagoya Math. J., 82, 131, 10.1017/S0027763000019322 Talagrand, 1995, Hausdorff measure of trajectories of multiparameter fractional Brownian motion, Ann. Probab., 23, 767, 10.1214/aop/1176988288 Xiao, 2009, Sample path properties of anisotropic Gaussian random fields, 145