Local nondeterminism and local times of general stochastic processes
Berman, Simeon M.
Annales de l'I.H.P. Probabilités et statistiques, Tome 19 (1983), p. 189-207 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1983-01-01
@article{AIHPB_1983__19_2_189_0,
     author = {Berman, Simeon M.},
     title = {Local nondeterminism and local times of general stochastic processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {19},
     year = {1983},
     pages = {189-207},
     mrnumber = {700709},
     zbl = {0516.60047},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1983__19_2_189_0}
}

Berman, Simeon M. Local nondeterminism and local times of general stochastic processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 19 (1983) pp. 189-207. http://gdmltest.u-ga.fr/item/AIHPB_1983__19_2_189_0/

[1] R.J. Adler, The Geometry of Random Fields, John Wiley and Sons, New York, 1981. | MR 611857 | Zbl 0478.60059

[2] S.M. Berman, Local times and sample function properties of stationary Gaussian processes. Trans. Amer. Math. Soc., t. 137, 1969, p. 277-299. | MR 239652 | Zbl 0184.40801

[3] S.M. Berman, Gaussian processes with stationary increments: local times and sample function properties. Ann. Math. Statist., t. 41, 1970, p. 1260-1272. | MR 272035 | Zbl 0204.50501

[4] S.M. Berman, Gaussian sample functions: uniform dimension and Holder conditions nowhere. Nagoya Math., J., t. 46, 1972, p. 63-86. | MR 307320 | Zbl 0246.60038

[5] S.M. Berman, Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J., t. 23, 1973, p. 69-94. | MR 317397 | Zbl 0264.60024

[6] S.M. Berman, Local times of stochastic processes with positive definite bivariate densities, Stochastic Processes Appl., t. 12, 1982, p. 1-26. | MR 632390 | Zbl 0471.60082

[7] S.M. Berman, Local times of stochastic processes which are subordinate to Gaussian processes. J. Multivariate Anal., t. 12, 1982, p. 317-334. | MR 666009 | Zbl 0502.60061

[8] A.S. Besicovitch, On existence of subsets of finite measure of sets of infinite measure. Indag. Math., t. 14, 1952, p. 339-344. | MR 48540 | Zbl 0046.28202

[9] J.M. Cuzick, Local nondeterminism and the zeros of Gaussian processes. Ann. Probability, t. 6, 1978, p. 72-84. | MR 488252 | Zbl 0374.60051

[10] B. Fristedt, Sample functions of stochastic processes with stationary independent increments. Advances in Probability, t. 3, 1973, p. 241-396. | MR 400406 | Zbl 0309.60047

[11] D. Geman and J. Horowitz, Occupation densities. Ann. Probability, t. 8, 1980, p. 1-67. | MR 556414 | Zbl 0499.60081

[12] J. Hawkes, On the comparison of measure functions. Math. Proc. Cambridge Phil. Soc., t. 78, 1975, p. 483-491. | MR 382605 | Zbl 0326.28006

[13] P. Levy, Sur certains processus stochastiques homogenes. Compositio Math., t. 7, 1939, p. 283-339. | JFM 65.1346.02 | Numdam | MR 919 | Zbl 0022.05903

[14] M.B. Marcus, Capacity of level sets of certain stochastic processes. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, t. 34, 1976, p. 279-284. | MR 420814 | Zbl 0368.60038

[15] S. Orey, Gaussian sample functions and the Hausdorff dimension of level crossings. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, t. 15, 1970, p. 249-256. | MR 279882 | Zbl 0196.19402

[16] E. Perkins, The exact Hausdorff measure of the level sets of Brownian motion. Z. Wahrscheinlichkeitstheorie Verw. Gebiete, t. 58, 1981, p. 373-388. | MR 639146 | Zbl 0458.60076

[17] L.D. Pitt, Local times for Gaussian vector fields, Indiana Univ. Math. J., t. 27, 1978, p. 309-330. | MR 471055 | Zbl 0382.60055

[18] S.J. Taylor, Sample path properties of processes with stationary independent increments. In Stochastic Analysis, John Wiley and Sons, New York, 1973. | MR 394893

[19] S.J. Taylor and J.G. Wendel, The exact Hausdorff measure of the zero set of a stable process. Z. Wahrscheinlichkeitstheorie Venw. Gebiete, t. 6, 1966, p. 170-180. | MR 210196 | Zbl 0178.52702

[20] H.F. Trotter, A property of Brownian motion paths. Illinois J. Math., t. 2, 1958, p. 425-432. | MR 96311 | Zbl 0117.35502