Overshoot in the Case of Normal Variables

Abstract

A new formula, in the form of an infinite series, is derived for the limiting expected excess over the boundary of a sum of independent and identically distributed normal variables as the positive mean goes to zero. The first order correction for small positive mean is also derived by the same method.

Key Words:

• Excess over stopping bound
• Expected excess
• Renewal theory

Acknowledgment

The hospitality extended to me by the Department of Statistics at the University of Washington, where part of the research in this paper was done, is hereby gratefully acknowledged.

Notes

Recommended by S. Chattopadhyay