On the Increments of Multidimensional Random Fields
Geman, Donald ; Zinn, Joel
Ann. Probab., Tome 6 (1978) no. 6, p. 151-158 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For a nondifferentiable random field $\{X_t: t \in \mathbb{R}^N\}$ with values in $\mathbb{R}^d$, it is often easy to check that with probability 1 $\lim \inf_{s\rightarrow t}\|X_s - X_t\|/\sigma(s, t) = 0$ and $\lim \sup_{s\rightarrow t}\|X_s - X_t\|/\sigma(s, t) = \infty$ for a.e. $t$, where $\sigma^2(s, t) = E\|X_s - X_t\|^2$. In this note we discuss the "proportion" of $s$'s near $t$ for which $\|X_s - X_t\|/\sigma(s, t)$ is small or large.
Publié le : 1978-02-14
Classification:  Random field,  approximate limit,  Gaussian process,  stationary increments,  60G10,  60G15,  60G17 
@article{1176995620,
     author = {Geman, Donald and Zinn, Joel},
     title = {On the Increments of Multidimensional Random Fields},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 151-158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995620}
}

Geman, Donald; Zinn, Joel. On the Increments of Multidimensional Random Fields. Ann. Probab., Tome 6 (1978) no. 6, pp.  151-158. http://gdmltest.u-ga.fr/item/1176995620/