From Elementary Probability to Stochastic Differential Equations with MAPLE®
By: by Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
Contributors: Kloeden, Peter; Ombach, Jerzy
Series: Universitext, 0172-5939; Universitext
Publisher: Springer Berlin Heidelberg; Imprint; Springer
Published: 2002
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 310
ISBN-13: 9783642561443
Subjects: Numerical analysis; Statistics; Algorithms; Mathematics; Distribution (Probability theory); Economics
Description: The authors provide a fast introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. The book is based on measure theory which is introduced as smoothly as possible. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, providing an overview and intuitive background for more advanced studies as well as some practical skills in the use of MAPLE in the context of probability and its applications. Although this book contains definitions and theorems, it differs from conventional mathematics books in its use of MAPLE worksheets instead of formal proofs to enable the reader to gain an intuitive understanding of the ideas under consideration. As prerequisites the authors assume a familiarity with basic calculus and linear algebra, as well as with elementary ordinary differential equations and, in the final chapter, simple numerical methods for such ODEs. Although statistics is not systematically treated, they introduce statistical concepts such as sampling, estimators, hypothesis testing, confidence intervals, significance levels and p-values and use them in a large number of examples, problems and simulations.
Table of contents: title: 1. Probability basics; title: 2. Measure and integral; title: 3. Random variables and distributions; title: 4. Parameters of distributions; title: 5. A tour of important distributions; title: 6. Numerical simulations and statistical inference; title: 7. Stochastic processes; title: 8. Stochastic calculus; title: 9. Stochastic differential equations; title: 10. Numerical methods of SDEs.