Sasha Cyganowski, Peter Kloeden, Jerzy Ombach

From Elementary Probability to Stochastic Differential Equations with MAPLE® (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 310
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642561443
• Artikelnr.: 53145989

Inhaltsangabe

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.

Rezensionen

From the reviews: "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 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 concern. 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." L'Enseignment Mathematique, Issue 1-2, Vol. 48, 2002, p.

"... The authors have done a good job. The material is didactically well presented, and motivations are given before definitions are stated. MAPLE, a computer algebra system, is used to illustrate the mathematics and help readers understand the concepts. ..."

Walter Gander, Journal of the American Statistical Association, March 2003, p. 254-255

"... This book is valuable as supplementary text to introductions into probability theory."

F.Hofbauer, Monatshefte für Mathematik 2003, Vol. 138, Issue 1

"... The aim of the book is to supplement conventional mathematical textbooks on probability and stochastics. The book serves its purpose very well. ..."

Evelyn Buckwar, Zentralblatt für Mathematik 987.60002

"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 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 concern. 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."

L'Enseignment Mathematique, Issue 1-2, Vol. 48, 2002, p. 20