Asymptotic Properties of Gaussian Processes

Qualls, Clifford; Watanabe, Hisao

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 580-596 / Harvested from Project Euclid

Résumé

We study separable mean zero Gaussian processes $X(t)$ with correlation $\rho (t, s)$ for which $1 - \rho (t, s)$ is asymptotic to a regularly varying (at zero) function of $|t - s|$ with exponent $0 < \alpha \leqq 2$. For such processes, we obtain the asymptotic distribution of the maximum of $X(t)$. This result is used to obtain a result for $X(t)$ as $t \rightarrow \infty$ similar to the so-called law of the iterated logarithm.

Publié le : 1972-04-14
Classification:

@article{1177692638,
     author = {Qualls, Clifford and Watanabe, Hisao},
     title = {Asymptotic Properties of Gaussian Processes},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 580-596},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692638}
}

Qualls, Clifford; Watanabe, Hisao. Asymptotic Properties of Gaussian Processes. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  580-596. http://gdmltest.u-ga.fr/item/1177692638/