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.

Inhalt

1 Probability Basics.- 2 Measure and Integral.- 3 Random Variables and Distributions.- 4 Parameters of Probability Distributions.- 5 A Tour of Important Distributions.- 6 Numerical Simulations and Statistical Inference.- 7 Stochastic Processes.- 8 Stochastic Calculus.- 9 Stochastic Differential Equations.- 10 Numerical Methods for SDEs.- Bibliographical Notes.- References.