1st Edition

Model Theory of Stochastic Processes Lecture Notes in Logic 14

By Sergio Fajardo, H. Jerome Keisler Copyright 2002
    140 Pages
    by A K Peters/CRC Press

    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.

    Introduction Chapter 1. Adapted distributions Chapter 2. Hyperfnite adapted spaces Chapter 3. Saturated spaces Chapter 4. Comparing stochastic processes Chapter 5. Defnability in adapted spaces Chapter 6. Elementary extensions Chapter 7. Rich adapted spaces Chapter 8. Adapted neometric spaces Chapter 9. Enlarging saturated spaces


    Sergio Fajardo Department of Mathematics, University of Los Andes, Bogota, Colombia. H. Jerome Keisler Department of Mathematics, University of Wisconsin, Madison, Wisconsin, USA.