Levy Processes

Rating:
Summary: A good overview of Levy processes and their applications.
Review: 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.