Jinqiao Duan. An Introduction to Stochastic Dynamics. New York, Cambridge University Press.

Jinqiao Duan. An Introduction to Stochastic Dynamics. New York, Cambridge University Press. Rigorous treatment of stochastic dynamical systems requires a high level of technical effort. This effort, however, discourages students and researchers of applied sciences. As many applied problems ask for this framework, there is a need for non‐technical introductions to this topic, which is exactly the point the present work aims to accomplish. The book does not intend to only show simulation techniques and informal interpretations of simulated results, but rather to communicate the proper mathematical tools. A balance between informal explanations and precise mathematical statements is achieved by simultaneously introducing a wide range of the basic mathematical structures while quoting the fundamental theorems without proof (but with appropriate literature hints). The mathematical techniques become clear in many examples on the one hand, and in proving less demanding theorems on the other hand. The book focuses on stochastic differential equations and their treatment, while branching processes and interacting particle processes are not covered.The preface indicates that a profound basic education in elementary stochastics is required, up to some ideas about stochastic differential equations. In my opinion, the book provides enough material to allow students and applied scientists to catch up without a deep prior insight into these topics, though some http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrics Wiley

Jinqiao Duan. An Introduction to Stochastic Dynamics. New York, Cambridge University Press.

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018, The International Biometric Society
ISSN
0006-341X
eISSN
1541-0420
D.O.I.
10.1111/biom.12854
Publisher site
See Article on Publisher Site

Abstract

Rigorous treatment of stochastic dynamical systems requires a high level of technical effort. This effort, however, discourages students and researchers of applied sciences. As many applied problems ask for this framework, there is a need for non‐technical introductions to this topic, which is exactly the point the present work aims to accomplish. The book does not intend to only show simulation techniques and informal interpretations of simulated results, but rather to communicate the proper mathematical tools. A balance between informal explanations and precise mathematical statements is achieved by simultaneously introducing a wide range of the basic mathematical structures while quoting the fundamental theorems without proof (but with appropriate literature hints). The mathematical techniques become clear in many examples on the one hand, and in proving less demanding theorems on the other hand. The book focuses on stochastic differential equations and their treatment, while branching processes and interacting particle processes are not covered.The preface indicates that a profound basic education in elementary stochastics is required, up to some ideas about stochastic differential equations. In my opinion, the book provides enough material to allow students and applied scientists to catch up without a deep prior insight into these topics, though some

Journal

BiometricsWiley

Published: Jan 1, 2018

References

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