Inequalities for first-exit probabilities and expected first-exit times of a random walk

Inequalities for first-exit probabilities and expected first-exit times of a random walk

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Article ID: iaor19971692
Country: United States
Volume: 12
Issue: 1
Start Page Number: 103
End Page Number: 120
Publication Date: Jan 1996
Journal: Communications in Statistics - Stochastic Models
Authors:
Abstract:

For the partial sum process of i.i.d. random variables the paper derives sequences of new upper and lower bounds for the probability that it will exit from a given compact interval to the left and for the expected first-exit time. The sequences are generated by the same iterative procedure starting from different initial values. They converge monotonically to the desired first-exit quantities at an exponential rate.

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