I. A Tutorial on Levy Processes. - Basic Results on Lévy Processes. - II. Distributional Pathwise and Structural Results. - Exponential Functionals of Lévy Processes. - Fluctuation Theory for Lévy Processes. - Gaussian Processes and Local Times of Symmetric Lévy Processes. - Temporal Change in Distributional Properties of Lévy Processes. - III. Extensions and Generalizations of Lévy Processes. - Lévy Processes in Stochastic Differential Geometry. - Lévy-Type Processes and Pseudodifferential Operators. - Semistable Distributions. - IV. Applications in Physics. - Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory. - Lévy Processes and Continuous Quantum Measurements. - Lévy Processes in the Physical Sciences. - Some Properties of Burgers Turbulence with White or Stable Noise Initial Data. - V. Applications in Finance. - Modelling by Lévy Processess for Financial Econometrics. - Application of Generalized Hyperbolic Lévy Motions to Finance. - Explicit Form and Path Regularity of Martingale Representations. - Interpretations in Terms of Brownian and Bessel Meanders of the Distribution of a Subordinated Perpetuity. - VI. Numerical and Statistical Aspects. - Maximum Likelihood Estimation and Diagnostics for Stable Distributions. - Series Representations of Lévy Processes from the Perspective of Point Processes. Language: English