Aimed at students and researchers in mathematics, communications engineering, and economics, this book describes the probabilistic structure of a Gaussian process in terms of its canonical representation (or its innovation process). Multiple Markov properties of a Gaussian process and equivalence problems of Gaussian processes are clearly presented. The authors' approach is unique, involving causality in time evolution and information-theoretic aspects. Because the book is self-contained and only requires background in the fundamentals of probability theory and measure theory, it would be suitable as a textbook at the senior undergraduate or graduate level.

Readership

Senior-level and graduate-level mathematics students. Students and researchers in communications engineering. Researchers in economics.

Reviews

"Each part of the exposition progresses from the simple to the more sophisticated, thus avoiding the perils of plunging the reader straight into the deep waters of the more advanced theory. No specialized knowledge is required on the part of the reader, other than a good command of the general theory of probability."

-- Mathematical Reviews

Table of Contents

• Foundations of probability theory and limit theorems
• Systems of Gaussian random variables
• Stationary Gaussian processes and their representations
• Canonical representation of Gaussian processes: General theory and multiplicity
• Multiple Markov Gaussian processes
• Equivalence of Gaussian processes
• Stochastic integrals and martingales