Lévy Processes and Stochastic Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Processes and Stochastic Calculus write by David Applebaum. This book was released on 2009-04-30. Lévy Processes and Stochastic Calculus available in PDF, EPUB and Kindle. Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Fluctuations of Lévy Processes with Applications
Fluctuations of Lévy Processes with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fluctuations of Lévy Processes with Applications write by Andreas E. Kyprianou. This book was released on 2014-01-09. Fluctuations of Lévy Processes with Applications available in PDF, EPUB and Kindle. Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Lévy Processes
Lévy Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lévy Processes write by Ole E Barndorff-Nielsen. This book was released on 2012-12-06. Lévy Processes available in PDF, EPUB and Kindle. A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays 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 Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy 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. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. 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 futurearch. 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 Lévy processes.
Malliavin Calculus for Lévy Processes with Applications to Finance
Malliavin Calculus for Lévy Processes with Applications to Finance - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Malliavin Calculus for Lévy Processes with Applications to Finance write by Giulia Di Nunno. This book was released on 2008-10-08. Malliavin Calculus for Lévy Processes with Applications to Finance available in PDF, EPUB and Kindle. This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.
Cambridge Tracts in Mathematics
Cambridge Tracts in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cambridge Tracts in Mathematics write by Jean Bertoin. This book was released on 1996. Cambridge Tracts in Mathematics available in PDF, EPUB and Kindle. This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.
