![]() … In my opinion this is a great book for self-study, as the exercises and solutions are a goldmine.” (Peter Rabinovitch, MAA Reviews, May, 2018) There are also many interesting detailed examples and discussions that elaborate on the theory. “The unique feature of this book is the vast amount of exercises and solutions (more than 200, according to the publisher), with detailed solutions - they are not just a one line hints. I am going to use it in my future teaching activities.” (Josep Vives, Mathematical Reviews, November, 2018) In summary, I find that this is an excellent and complete book on stochastic calculus for master's level students. ![]() This aspect can be very useful for professors who plan to use the book for teaching. … The book includes plenty of exercises, all of them completely and extensively solved in the appendix. “This book is an excellent and quite complete course of stochastic calculus at the master's degree level. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. ![]() The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. It is the only textbook on the subject to include more than two hundred exercises with complete solutions.Īfter explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. This book covers models in mathematical finance, biology and engineering. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. It contains many solved examples and exercises making it suitable for self study. It is also suitable for researchers to gain working knowledge of the subject. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. ![]() This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. ![]() Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. In finance, the stochastic calculus is applied to pricing options by no arbitrage. It also gives its main applications in finance, biology and engineering. This book presents a concise and rigorous treatment of stochastic calculus. ![]()
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