Large Deviations for Boundary Crossing Probabilities
Siegmund, D.
Ann. Probab., Tome 10 (1982) no. 4, p. 581-588 / Harvested from Project Euclid
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For random walks $s_n, n = 1,2, \cdots$ whose distribution can be imbedded in an exponential family, a method is described for determining the asymptotic behavior as $m \rightarrow \infty$ of $P\{s_n > m c(n/m) \quad\text{for some}\quad n < m\mid s_m = m \mu_0\}, \quad\mu_0 < c(1).$ Applications are given to the distribution of the Smirnov statistic and to modified repeated significance tests.
Publié le : 1982-08-14
Classification:  First passage distribution,  stopping rule,  large deviation,  sequential test,  60F05,  60J15,  62L10 
@article{1176993768,
     author = {Siegmund, D.},
     title = {Large Deviations for Boundary Crossing Probabilities},
     journal = {Ann. Probab.},
     volume = {10},
     number = {4},
     year = {1982},
     pages = { 581-588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993768}
}

Siegmund, D. Large Deviations for Boundary Crossing Probabilities. Ann. Probab., Tome 10 (1982) no. 4, pp.  581-588. http://gdmltest.u-ga.fr/item/1176993768/