For good reasons the theory of stochastic differential equations (SDEs) is recognized as one of the most beautiful mathematical theories. In addition, SDEs are fundamental and irreplaceable tools in modelling a variety of complex phenomena which are both dynamic and random.

Since the SDEs that are used as models are usually non-linear, we rarely enjoy having explicit solutions to problems of interest. Among the challenges are statistical inference problems which typically are difficult analytic problems. Hence it is important to develop algorithms for approximate solutions. To have good speed of convergence of the algorithms is one of the primary goals. Modern technology helps in the implementation and also in producing and using simulated data.

The author of this book has made an essential contribution in the area of statistical inference for SDEs. In addition, he is one of the contributors to the development of the language R in a statistical environment. Thus, he is the ideal person to write a book on one side to explain well SDE models and their properties, and on the other side to suggest the most appropriate R programs for solving the problems.

The author tells us that the book is addressed to practitioners. Perhaps he has in mind well-prepared applied scientists with excellent knowledge and experience in stochastic processes, in particular stochastic analysis.

The book covers well-chosen material distributed in four chapters: 1, ‘Stochastic processes and SDE’; 2, ‘Numerical methods for SDE’; 3, ‘Parametric estimation’; 4, ‘Miscellaneous topics’. Also included are Appendix A, ‘A brief excursus into R’, and Appendix B, ‘The sde package’. There is a comprehensive list of references and an index.

It is remarkable to see so wide a range of topics all discussed in a master style. What makes this book different from other books in applied stochastics is the inclusion of R efficient codes for simulation schemes of SDEs and related estimation methods based on discrete sampled observations. The author has done a great job!

The book will be of interest to applied stochasticians, especially those who are involved in the popular area of stochastic financial modelling.

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