On the Maximum of a Stationary Independent Increment Process
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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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 Mt , the maximum value that such a process attains by time t . By using renewal theoretic methods the author obtains results about Mt . In particular the author shows that if mu, the mean drift of the process, is positive, then Mtt converges to mu, and EMt h - Mt to h mu.
- Statistics and Probability