Olav Kallenberg Livres

Exploring the foundational symmetries of probability theory, this book delves into contractability, exchangeability, and rotatability, highlighting their invariance under different transformations. Building on de Finetti's groundbreaking work, it presents a wealth of results that reveal surprising connections between these symmetries and other probability domains. Aimed at graduate students and researchers, the text is accessible with a basic understanding of probability, and includes comprehensive references for further exploration in real analysis and probability.

A study of the foundations of modern probability, covering topics such as stochastic integrals and quadratic variation, martingales and optional times, Feller processes and semigroups, and Poisson and pure jump type Markov processes.

Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.