For a random walk with mean zero and variance one, a conditional limit theorem is proved under conditions on the path until it for the first time becomes negative. This gives a generalization of a limit theorem for random walk conditioned to stay positive which was considered by Iglehart and others. It has an application to get a tail formula of the d.f. of the maximum for a stopped random walk.
Publié le : 1983-02-14
Classification:
Random walk,
conditional limit theorem,
excursions of reflecting Brownian motion,
60J15,
60F17
@article{1176993658,
author = {Shimura, Michio},
title = {A Class of Conditional Limit Theorems Related to Ruin Problem},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 40-45},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993658}
}
Shimura, Michio. A Class of Conditional Limit Theorems Related to Ruin Problem. Ann. Probab., Tome 11 (1983) no. 4, pp. 40-45. http://gdmltest.u-ga.fr/item/1176993658/