For random walks $\{S_n\}$ whose distribution can be embedded in an exponential family, large-deviation approximations are obtained for the probability that $\max_{0\leq i < j\leq m}(S_j - S_i) \geq b$ (i) conditionally given $S_m$ and (ii) unconditionally. The method used in the conditional case seems applicable to maxima of a reasonably large class of random fields. For the unconditional probability a more special argument is used, and more precise results obtained.
Publié le : 1988-04-14
Classification:
Large deviations,
random field,
CUSUM test,
60F10,
60G60,
60K05,
62N10
@article{1176991769,
author = {Siegmund, David},
title = {Approximate Tail Probabilities for the Maxima of Some Random Fields},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 487-501},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991769}
}
Siegmund, David. Approximate Tail Probabilities for the Maxima of Some Random Fields. Ann. Probab., Tome 16 (1988) no. 4, pp. 487-501. http://gdmltest.u-ga.fr/item/1176991769/