Brownian Motion, the Fredholm Determinant, and Time Series Analysis - Tanaka, Katsuto
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Erscheint vorauss. 31. Dezember 2024
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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…mehr

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Produktbeschreibung
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.
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Autorenporträt
Katsuto Tanaka is Professor Emeritus at Hitotsubashi University, Tokyo. He is a recipient of the Tjalling C. Koopmans Econometric Theory Prize (1996), the Japan Statistical Society Prize (1998), and the Econometric Theory Award (1999). He previously authored 'Time Series Analysis' (First Edition 1996, Second Edition 2017) and six statistics and econometrics books in Japanese.