Model Theory Of Stochastic Processes

Model Theory of Stochastic Processes

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.

Model Theory of Stochastic Processes

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.

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