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 2004-07-05. Lévy Processes and Stochastic Calculus available in PDF, EPUB and Kindle. Publisher Description
Lévy Processes and Stochastic Calculus
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.
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.
Brownian Motion and Stochastic Calculus
Brownian Motion 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 Brownian Motion and Stochastic Calculus write by Ioannis Karatzas. This book was released on 2014-03-27. Brownian Motion and Stochastic Calculus available in PDF, EPUB and Kindle. A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and 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.
