Geodesic
Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 123-127

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a real stochastic process. We localize S. M. Berman's formulation on the local nondeterminism of X to a fixed level. With this localized idea, we prove that, for large classes of Gaussian and Markov X, at each x the level set X(t, w) = x has infinite Hausdorff φ - measure (φ is certain measure function) for w in a set of positive probability.
DOI : 10.4153/CMB-1991-020-9
Mots-clés : 60G17. 
Shieh, Narn-Rueih. Conditional Local Nondeterminism and Hausdorff Measure of Level Sets. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 123-127. doi: 10.4153/CMB-1991-020-9
@article{10_4153_CMB_1991_020_9,
     author = {Shieh, Narn-Rueih},
     title = {Conditional {Local} {Nondeterminism} and {Hausdorff} {Measure} of {Level} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {123--127},
     year = {1991},
     volume = {34},
     number = {1},
     doi = {10.4153/CMB-1991-020-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-020-9/}
}
TY  - JOUR
AU  - Shieh, Narn-Rueih
TI  - Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 123
EP  - 127
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-020-9/
DO  - 10.4153/CMB-1991-020-9
ID  - 10_4153_CMB_1991_020_9
ER  - 
%0 Journal Article
%A Shieh, Narn-Rueih
%T Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
%J Canadian mathematical bulletin
%D 1991
%P 123-127
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-020-9/
%R 10.4153/CMB-1991-020-9
%F 10_4153_CMB_1991_020_9

[1] 1. Berman, S. M., Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973), 69–94. Google Scholar

[2] 2. Berman, S. M., Local nondeterminism and local times of general stochastic processes, Ann. Inst. Henri Poincaré XIX(1983), 189–207. Google Scholar

[3] 3. Berman, S. M., The modulator of the local time, Comm. on Pure and Applied Math. XLI(1988), 121–132. Google Scholar

[4] 4. Fristedt, B. and Pruitt, W., Lower function for increasing random walks and subordinators, Z. Wahrscheinlichkeitstheorie verw. Gebiete 18 (1971), 167–182. Google Scholar

[5] 5. Kahane, J. P., Some random series of functions. D. C. Heath, 1968. Google Scholar

[6] 6. Marcus, M. B., Capacity of level sets of certain stochastic processes Z. Wahrscheinlichkeitstheorie verw. Gebiete 34 (1976), 279–284. Google Scholar

Cité par Sources :