Abstract
We review the question of the extreme values attained by a random process. We relate it to level crossings to one boundary (first-passage problems) as well as to two boundaries (escape problems). The extremes studied are the maximum, the minimum, the maximum absolute value, and the range or span. We specialize in diffusion processes and present detailed results for the Wiener and Feller processes.
- Received 23 January 2014
DOI:https://doi.org/10.1103/PhysRevE.89.042106
©2014 American Physical Society