Sojourns and Extremes of Stochastic Processes is a research monograph in the area of probability theory. During the past thirty years Berman has made many contributions to the theory of the extreme values and sojourn times of the sample functions of broad classes of stochastic processes. These processes arise in theoretical and applied models, and are presented here in a unified exposition.
Table of Contents
1. Sojourn Time Distributions 2. Survey of the Normal Distribution 3. Stationary Gaussian Processes on a Finite Interval 4. Processes with Stationary Independent Increments 5. Diffusion Processes 6. Random Walk and Birth-and-Death Processes 7. Stationary Gaussian Processes on a Long Interval 8. Central Limit Theorems 9. Extremes of Gaussian Sequences and Diffusion Processes 10. Maximum of a Gaussian Process 11. Other Gaussian Sequences and Markov Random Fields 12. Processes (X, f(t)) with Orthogonally Invariant X