An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes

Аннотация

They are meant to be an introduction to what I call the "modern" theory of sample path properties of Gaussian processes, where by "modern" I mean a theory based on concepts such as entropy and majorising measures. They are directed at an audience that has a reasonable probability background, at the level of any of the standard texts (Billingsley, Breiman, Chung, etc.). It also helps if the reader already knows something about Gaussian processes, since the modern treatment is very general and thus rather abstract, and it is a substantial help to one's understanding to have some concrete examples to hang the theory on. To help the novice get a feel for what we are talking about, Chapter 1 has a goodly collection of examples.