Convergence Rates for Probabilities of Moderate Deviations for Sums of Random Variables with Multidimensional Indices
Gut, Allan
Ann. Probab., Tome 8 (1980) no. 6, p. 298-313 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For a set of i.i.d. random variables indexed by $Z^d_+, d \geqslant 1$, the positive integer $d$-dimensional lattice points, convergence rates for moderate deviations are derived, i.e., the rate of convergence to zero of, for example, certain tail probabilities of the partial sums, are determined. As an application we obtain results on the integrability of last exit times (in a certain sense) and the number of boundary crossings of the partial sums.
Publié le : 1980-04-14
Classification:  i.i.d. random variables,  multidimensional index,  convergence rate,  law of the iterated logarithm,  last exit time,  the number of boundary crossings,  60F15,  60G50 
@article{1176994778,
     author = {Gut, Allan},
     title = {Convergence Rates for Probabilities of Moderate Deviations for Sums of Random Variables with Multidimensional Indices},
     journal = {Ann. Probab.},
     volume = {8},
     number = {6},
     year = {1980},
     pages = { 298-313},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994778}
}

Gut, Allan. Convergence Rates for Probabilities of Moderate Deviations for Sums of Random Variables with Multidimensional Indices. Ann. Probab., Tome 8 (1980) no. 6, pp.  298-313. http://gdmltest.u-ga.fr/item/1176994778/