This book 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.
Table of Contents
Dedication, Introduction, Chapter 1: Adapted Distributions, Chapter 2: Hyperfinite Adapted Spaces, Chapter 3: Saturated Spaces, Chapter 4: Comparing Stochastic Processes, Chapter 5: Definability in Adapted Spaces, Chapter 6: Elementary Extensions, Chapter 7: Rich Adapted Spaces, Chapter 8: Adapted Neometric Spaces, Chapter 9: Enlarging Saturated Spaces, References
Fajardo\, Sergio; Keisler\, H. Jerome