Probability Estimates for the Small Deviations of $d$-Dimensional Random Walk
Griffin, Philip S.
Ann. Probab., Tome 11 (1983) no. 4, p. 939-952 / Harvested from Project Euclid
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Let $X_1, X_2, \cdots$ be a sequence of independent, identically distributed random variables taking values in $\mathbb{R}^d$ and $S_n = X_1 + \cdots + X_n$. For a large class of distributions we obtain estimates for the probability that $S_n$ is in a ball centered at the origin. Such an estimate would follow from a local limit theorem if $X_1$ were in the domain of attraction of a stable law.
Publié le : 1983-11-14
Classification:  Probability estimate,  local limit theorem,  60G50,  60E15 
@article{1176993443,
     author = {Griffin, Philip S.},
     title = {Probability Estimates for the Small Deviations of $d$-Dimensional Random Walk},
     journal = {Ann. Probab.},
     volume = {11},
     number = {4},
     year = {1983},
     pages = { 939-952},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993443}
}

Griffin, Philip S. Probability Estimates for the Small Deviations of $d$-Dimensional Random Walk. Ann. Probab., Tome 11 (1983) no. 4, pp.  939-952. http://gdmltest.u-ga.fr/item/1176993443/