Bøger af Ole E Barndorff-Nielsen

A Levy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. The need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Levy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Levy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. It collects articles written by leading experts that will appeal to the non-specialist. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for future research. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lvy processes.

A few preliminaries 2 1. Likelihood and auxiliary statistics 1. Likelihood 4 1. Moments and cumulants of log likelihood derivatives 10 1. Marginal and conditional likelihood 15 * 1. Combinants, auxiliaries, and the p -model 19 1. Pseudo likelihood, profile likelihood and modified 30 profile likelihood 1.