On the Maximum of a Stationary Independent Increment Process
Abstract
A stationary independent increment process is the continuous time analogue of the discrete random walk, and, as such, has a wide variety of applications. In this paper the author considers M(t) , the maximum value that such a process attains by time t . By using renewal theoretic methods the author obtains results about M(t) . In particular the author shows that if mu, the mean drift of the process, is positive, then M(t)/t converges to mu, and E(M(t + h) - M(t)) to h mu.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1971
- Accession Number
- AD0734133
Entities
People
- Sheldon M. Ross
Organizations
- University of California, Berkeley