Mean first-passage time for random-walk span: Comparison between theory and numerical experiment

The predictions of a recent theoretical analysis developed by Weiss, DiMarzio, and Gaylord [J. Stat. Phys. 42, 567 (1986)] on the mean first-passage time for a random-walk span in a free system to reach a given target span S are compared with the results of numerical simulation. Although the results are in good agreement qualitatively, a systematic quantitative discrepancy is found between theoretical predictions and experimental results in the large but finite S region, thus indicating the need for further theoretical analysis of the problem. Numerical results are also obtained in the case of a random-walk process driven by Gaussian colored noise.