Model Theory of Stochastic Processes

Sergio Fajardo, H. Jerome Keisler

• Publisher: Cambridge University Press
• eBook ISBN: 9781108619264
• Topic: Mathematics
• Subtopic: Logic in Mathematics
• Index: Mathematics

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourteenth publication in the Lecture Notes in Logic series, Fajardo and Keisler present new research combining probability theory and mathematical logic. It is a general study of stochastic processes using ideas from model theory, a key central theme being the question, 'When are two stochastic processes alike?' The authors assume some background in nonstandard analysis, but prior knowledge of model theory and advanced logic is not necessary. This volume will appeal to mathematicians willing to explore new developments with an open mind.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Table of contents
• INTRODUCTION
• 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
• REFERENCES
• Index