Steen Thorbjørnsen - Böcker

This textbook provides a thorough exposition of measure and integration theory in a style that is very detailed and thus easy to follow and understand. While breaking down argumentation to simple steps and maintaining a consistent exposition, the book presents the theory on a high level of scientific rigor and generality.Although the book covers a wide spectrum of topics, it leads to a path in functional analysis and probability theory. Thus, a full chapter on measures with densities, including Lebesgue decomposition and Radon-Nikodym's theorem, is included, as well as a chapter on transformation of measures, which is a crucial topic in probability theory. Chapters on Hilbert spaces and the Fourier transform prepare the way for a direction in functional analysis. The book features also a presentation of the Cauchy-Stieltjes transform, which is an alternative to the Fourier transform and highly used in some branches of mathematics, like mathematical physics and random matrix theory.The textbook has been tested for more than a decade in classrooms. Its style is particularly aimed at students who prefer a step-by-step approach, making it suitable for self-study as well. Appendices that cover all needed background material on real numbers, countability and metric spaces, are provided.

Collecting together twenty-three self-contained articles, this volume presents the current research of a number of renowned scientists in both probability theory and statistics as well as their various applications in economics, finance, the physics of wind-blown sand, queueing systems, risk assessment, turbulence and other areas.The contributions are dedicated to and inspired by the research of Ole E. Barndorff-Nielsen who, since the early 1960s, has been and continues to be a very active and influential researcher working on a wide range of important problems.The topics covered include, but are not limited to, econometrics, exponential families, Lévy processes and infinitely divisible distributions, limit theory, mathematical finance, random matrices, risk assessment, statistical inference for stochastic processes, stochastic analysis and optimal control, time series, and turbulence. The book will be of interest to researchers and graduate students in probability, statistics and their applications.

Collecting together twenty-three self-contained articles, this volume presents the current research of a number of renowned scientists in both probability theory and statistics as well as their various applications in economics, finance, the physics of wind-blown sand, queueing systems, risk assessment, turbulence and other areas.The contributions are dedicated to and inspired by the research of Ole E. Barndorff-Nielsen who, since the early 1960s, has been and continues to be a very active and influential researcher working on a wide range of important problems.The topics covered include, but are not limited to, econometrics, exponential families, Lévy processes and infinitely divisible distributions, limit theory, mathematical finance, random matrices, risk assessment, statistical inference for stochastic processes, stochastic analysis and optimal control, time series, and turbulence. The book will be of interest to researchers and graduate students in probability, statistics and their applications.