Brownian Motion, the Fredholm Determinant, and Time Series Analysis

Brownian motion is an important topic in various applied fields where the analysis of random events is necessary. Introducing Brownian motion from a statistical viewpoint, this detailed text examines the distribution of quadratic plus linear or bilinear functionals of Brownian motion and demonstrates the utility of this approach for time series analysis. It also offers the first comprehensive guide on deriving the Fredholm determinant and the resolvent associated with such statistics. Presuming only a familiarity with standard statistical theory and the basics of stochastic processes, this book brings together a set of important statistical tools in one accessible resource for researchers and graduate students. Readers also benefit from online appendices, which provide probability density graphs and solutions to the chapter problems.

• Introduces Brownian motion from a statistical viewpoint and uses statistics based on its quadratic functionals to compute distributions
• Defines the Fredholm determinant in connection with Brownian motion and explains how to derive in detail using various examples
• Discusses time series analysis from a distributional point of view, combining Brownian motion and the Fredholm determinant