Lecture Notes in Logic 14

Model Theory of Stochastic Processes

Sergio Fajardo, H. Jerome Keisler

Year: 2002
ISBN: 1-56881-172-1
150 pages. Paperback.

Year: 2002
ISBN: 1-56881-167-5
150 pages. Hardcover.

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This monograph presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them. The book is accessible to researchers in probability, model theory, and nonstandard analysis.

Table of Contents

  1. Adapted Distributions
  2. Hyperfinite Adapted Spaces
  3. Saturated Spaces
  4. Comparing Stochastic Processes
  5. Definability in Adapted Spaces
  6. Elementary Extensions
  7. Rich Adapted Spaces
  8. Adapted Neometric Spaces
  9. Enlarging Saturated Spaces