Wald's Equation for a Class of Denormalized $U$-Statistics
Chow, Y. S. ; de la Pena, V. H. ; Teicher, H.
Ann. Probab., Tome 21 (1993) no. 4, p. 1151-1158 / Harvested from Project Euclid
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Under suitable conditions on a stopping time $T$ and zero mean i.i.d. random variables $\{X_n, n \geq 1\}$, a Wald-type equation $ES_{k, T} = 0$ is obtained where $S_{k, n}$ is the sum of products of $k$ of the $X$'s with indices from 1 to $n$. This, in turn, is utilized to obtain information about the moments of $T_k = \inf\{n \geq k: S_{k, n} \geq 0\}$ and $W_c = \inf\{n \geq 2: S^2_{1, n} > c\sum^n_{j = 1}X^2_j\}, c > 0$.
Publié le : 1993-04-14
Classification:  Wald's equation,  stopping times,  martingale inequalities,  60F99 
@article{1176989285,
     author = {Chow, Y. S. and de la Pena, V. H. and Teicher, H.},
     title = {Wald's Equation for a Class of Denormalized $U$-Statistics},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 1151-1158},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989285}
}

Chow, Y. S.; de la Pena, V. H.; Teicher, H. Wald's Equation for a Class of Denormalized $U$-Statistics. Ann. Probab., Tome 21 (1993) no. 4, pp.  1151-1158. http://gdmltest.u-ga.fr/item/1176989285/