Sample Moduli for Set-Indexed Gaussian Processes
Alexander, Kenneth S.
Ann. Probab., Tome 14 (1986) no. 4, p. 598-611 / Harvested from Project Euclid
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Sample path behavior is studied for Gaussian processes $W_p$ indexed by classes $\mathscr{L}$ of subsets of a probability space $(X, \mathscr{A}, P)$ with covariance $EW_P(A)W_P(B) = P(A \cap B)$. A function $\psi$ is found in some cases such that $\lim \sup_{t\rightarrow 0}\sup\{|W_P(C)|/\psi(P(C)): C \in \mathscr{L}, P(C) \leq t\} = 1$ a.s. This unifies and generalizes the LIL and Levy's Holder condition for Brownian motion, and some results of Orey and Pruitt for the Brownian sheet.
Publié le : 1986-04-14
Classification:  Gaussian process,  set-indexed process,  sample modulus,  Vapnik-Cervonenkis class,  60G15,  60G17 
@article{1176992533,
     author = {Alexander, Kenneth S.},
     title = {Sample Moduli for Set-Indexed Gaussian Processes},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 598-611},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992533}
}

Alexander, Kenneth S. Sample Moduli for Set-Indexed Gaussian Processes. Ann. Probab., Tome 14 (1986) no. 4, pp.  598-611. http://gdmltest.u-ga.fr/item/1176992533/