McCauley, Joseph L. Stochastic calculus and differential equations for physics and finance. (English) Zbl 1321.60002 Cambridge: Cambridge University Press (ISBN 978-0-521-76340-0/hbk; 978-1-139-01946-0/ebook). xi, 206 p. (2013). This book presents stochastic calculus used for the description of stochastic processes. These are applied, e.g., in physics or finance and often used by practitioners. Stochastic processes in this book are described by Itô calculus and Fokker-Planck equations in parallel, where the author focuses on nonstationary processes and general martingales.The book contains 15 chapters:1. Random variables and probability distributions2. Martingales, Markov, and nonstationarity3. Stochastic calculus4. Itō processes and Fokker-Planck equations5. Self-similar Itō processes6. Fractional Brownian motion7. Kolmogorov’s PDEs and Chapman-Kolmogorov equation8. Non-Markov Itō processes9. Black-Scholes, martingales, and Feynman-Kac10. Stochastic calculus with martingales11. Statistical physics and finance12. Introduction to new financial economics13. Statistical ensembles and time-series analysis14. Econometrics15. SemimartingalesEach chapter is divided into several sections and subsections and ends with some exercises. Alas, there are no solutions at the end of the book.The book gives a good introduction to stochastic calculus and is a helpful supplement to other well-known books on this topic. It may be recommended to graduate students in finance, stochastic analysis and physics, as well as practitioners of this field. Reviewer: Oliver Janke (Berlin) Cited in 3 Documents MSC: 60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory 60H05 Stochastic integrals 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G18 Self-similar stochastic processes 60G22 Fractional processes, including fractional Brownian motion 60H30 Applications of stochastic analysis (to PDEs, etc.) 60G44 Martingales with continuous parameter 60G48 Generalizations of martingales 60J60 Diffusion processes 35Q84 Fokker-Planck equations 60K35 Interacting random processes; statistical mechanics type models; percolation theory 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P10 Applications of statistics to biology and medical sciences; meta analysis 91G80 Financial applications of other theories 91G70 Statistical methods; risk measures Keywords:stochastic calculus; stochastic differential equations; Itō prosesses; Fokker-Planck equations; Kolmogorov PDEs; martingales; semi-martingales; fractional Brownian motion; mathematical finance; econometrics; statistical physics; time-series analysis PDFBibTeX XMLCite \textit{J. L. McCauley}, Stochastic calculus and differential equations for physics and finance. Cambridge: Cambridge University Press (2013; Zbl 1321.60002) Full Text: DOI