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.
 
Year: 2002   ISBN: 1-56881-172-1  
Price: $32
150 pages.   Paperback.
BUY NOW

Year: 2002   ISBN: 1-56881-167-5  
Price: $70
150 pages.   Hardcover.
BUY NOW

Table of Contents

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