The fascination of probability, statistics and their applications [electronic resource] : in honour of Ole E. Barndorff-Nielsen /
Podolskij, Mark.editor.
Stelzer, Robert.editor.
Thorbjørnsen, Steen.editor.
Veraart, Almut E. D.editor.
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.  .
Description based upon print version of record.
Preface; Ole E. Barndorff-Nielsen's Scientific Achievements; Contents; On the Size Distribution of Sand; 1 Introduction; 2 The Model and the Size-Distribution; 3 Interpretation of the Size Distribution Parameters; 4 Discussion; 5 Conclusion; References; From Wind-Blown Sand to Turbulence  and Back; 1 Introduction; 2 The Deterministic Navier-Stokes Equations; 2.1 Reynolds Decomposition; 2.2 Solution of the Stochastic Navier-Stokes; 3 The Kolmogorov-Obukhov-She-Leveque Scaling; 3.1 Computation of the Structure Functions; 3.2 The First Few Structure Functions
3.3 The Invariant Measure of the Stochastic Navier-Stokes3.4 The Differential Equation for the PDF; 4 The Probability Density Function; 4.1 The Generalized Hyperbolic Distributions; 5 The PDF of Turbulence; References; Modelling Turbulent Time Series  by BSS-Processes; 1 Introduction; 2 Stylised Features of Turbulent Time Series; 3 Modelling Framework; 3.1 The Cascade Model for the Turbulent Energy Dissipation; 3.2 A Stochastic Model for Turbulent Velocity Time Series; 4 Simulation Results; 4.1 Model Performance; 4.2 Simulation of BSS Processes; 4.3 Estimation Procedure; 5 Conclusion
ReferencesAssociated Natural Exponential Families  and Elliptic Functions; 1 Foreword; 2 Retrieving an NEF from Its Variance Function; 3 Associated Natural Exponential Families; 3.1 Examples of Associated Probabilities; 4 Discussion and Easy Cases for (Am4+Bm2+C)1/2; 4.1 The Case A=0; 4.2 The Case C=0; 4.3 The Case B2-4AC=0; 4.4 Ax2+Bx+C Cannot Have Simple Roots on (0,infty); 4.5 The Splitting of the Elliptic Variances in Three Cases; 5 The Elliptic Cases: The Case -1leqk20; 8 The Family F; 9 Conclusion: General Elliptic Variances
ReferencesCumulants and Bartlett Identities  in Cox Regression; 1 Introduction; 2 The Bartlett Identities, the Bartlett Factor, and Other Likelihood Quantities; 3 Bartlett Identities for Partial Likelihood; 4 The Cox Model; 5 Cumulants for Partial Likelihood; 6 Approximation and Estimation of the Cumulants; 7 Conclusion; References; Exchangeability and Infinite Divisibility; 1 Introduction; 2 Infinitely Divisible Exchangeable Distributions; 3 Matrices that Preserve Exchangeability; 4 Exchangeability Preserving Transformations
5 Exchangeability Preserving Transformations  Based on Discrete Time6 Exchangeability Preserving Transformations  Based on Continuous Time; References; Lévy Copulas: Review of Recent Results; 1 Introduction; 2 A Primer on Lévy Copulas; 3 Monte Carlo Simulation of Lévy Processes with a Specified Lévy Copula; 4 Statistical Estimation Techniques; 5 Lévy Copulas and Multivariate Regular Variation; 6 Risk Management Applications; 7 Conclusion; References; Weak Stationarity of Ornstein-Uhlenbeck Processes with Stochastic Speed of Mean Reversion; 1 Introduction
2 Generalised Ornstein-Uhlenbeck Processes
Includes bibliographical references at the end of each chapters.
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.  .
Probabilities.
Economics, Mathematical .
Statistics .
Probability Theory and Stochastic Processes.
Quantitative Finance.
Statistical Theory and Methods.