Lévy Processes: Theory and Applications by Ole E Barndorff-Nielsen (PDF)

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Preface I. A tutorial on Lévy processes Sato, K.: Basic results on Lévy processes II. Distributional, pathwise and structural results Carmona, P. / Petit, F. / Yor, M.: Exponentials functionals of Levy processes Doney, R.: Fluctuation theory for Levy processes Marcus, M.B. / Rosen, J.: Gaussian processes and the local times of symmetric Lévy processes Watanabe, T.: Temporal change in distributional properties of Lévy processes III: Extensions and generalisations of Lévy processes Applebaum, D.: Lévy processes in stochastic differential geometry Jac. / Schilling, R.L.: Lévy-type processes and pseudo-differential operators Maejima, M.: Semi-stable distributions IV. Applications in physics Albeverio, S. / Rüdiger, B. / Wu, J-L.: Analytic and probabilistic aspects of Lévy processes and fields in quantum theory Holevo, A.S.: Lévy processes and continuous quantum measurements Woyczynski, W.A.: Lévy processes in the physical sciences Bertoin, J.: Some properties of Burgers turbulence with white or stable noise V. Applications in finance Barndorff-Nielsen, O.E / Shepard, N.: Modelling by Lévy processes for financial econometrics Eberlein, E.: Application of generalized hyperbolic Lévy motions to finance Ma, J. / Protter, P. / Zhang, J: Explicit form and path regularity of martingale representation Yor, M.: Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity VI. Numerical and statistical aspects Nolan, J.P.: Maximum likelihood estimation and diagnostics for stable distributions Rosinski, J.: Series representations of Lévy processes from the perspective of point processes

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is the outgrowth of the international conference on Levy processes and applications organized by Ole BARNDORFFF NIELSEN and others in Aarhus, Denmark a few years ago. However, it is not a classical conference proceedings volume and the chapters are written in clear, pedagogical format so the book is in fact a nice reference on theory and applications of Levy processes for anyone interested in this field. While it does not claim to be exhaustive and for many details and proofs the reader is refered to papers and treatises, it gives an interesting view of applications of Levy processes.The introductory chapters (parts I and II) are very well written and give the minimum mathematical knowledge necessary for understanding the following chapters.Part IV ( applications in physics )is particularly weak:while this is probably the field where Levy processes have been most widely used, the applications presented are at most anecdotical ; they do not include the most well known applications which include laser cooling and disordered systems.The chapter called “Levy processes in the physical sciences”,written by a mathematical physicist and supposed to give an overview on this topic, only contains reference to work by the author of the chapter and gives the (wrong) impression that there is no other work in physics related to Levy processes.The part on applications to mathematical finance is nicely structured and contains new material on stochastic volatility models driven by Levy processes, due to Barndorff Nielsen and Shephard.Overall, what is missing is perhaps some statistical material on inference methods and more material on numerical methods (the last part on this topic is too short.However this book remains a very useful reference for researchers and graduate students interested in Levy processes.

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