Open Access
February, 1983 A Class of Conditional Limit Theorems Related to Ruin Problem
Michio Shimura
Ann. Probab. 11(1): 40-45 (February, 1983). DOI: 10.1214/aop/1176993658


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.


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Michio Shimura. "A Class of Conditional Limit Theorems Related to Ruin Problem." Ann. Probab. 11 (1) 40 - 45, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0506.60066
MathSciNet: MR682799
Digital Object Identifier: 10.1214/aop/1176993658

Primary: 60J15
Secondary: 60F17

Keywords: conditional limit theorem , excursions of reflecting Brownian motion , Random walk

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
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