Brownian Motion, the Fredholm Determinant, and Time Series Analysis

Introducing Brownian motion from a statistical viewpoint, this text gathers many important statistical tools in one accessible resource for researchers and graduate students. In particular, it explores how to derive the distribution of various statistics arising in time series analysis that are the quadratic functionals of Brownian motion.

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.