%0 Book %1 gardiner2004handbook %A Gardiner, C. W. %B Springer Series in Synergetics %C Berlin %D 2004 %I Springer-Verlag %K SDE reference %P xviii+415 %T Handbook of stochastic methods for physics, chemistry and the natural sciences %V 13 %X (MR) The second edition has been reviewed Handbook of stochastic methods, 1985; MR0858704 (87i:00033). This third edition includes a chapter on the numerical treatment of stochastic differential equations but the chapter on quantum Markov processes has been deleted because it had become obsolete. (For an updated treatment of this material see C. W. Gardiner and P. Zoller, Quantum noise, Second edition, Springer, Berlin, 2000; MR1736115 (2003f:81298).) This book fills a gap between mathematically oriented expositions of the theories of stochastic processes and stochastic differential equations on the one hand and applications to certain fields (e.g., in engineering) on the other. It provides stochastic methods nowadays frequently used in statistical and quantum physics, theoretical chemistry, and electronics. Among other things the author tries to give (and succeeds in giving) an audience of nonprobabilists insight into the seemingly inaccessible Itô calculus. The readership is intended to consist of theoretical physicists and chemists, but the reviewer is sure that engineers and mathematicians working in applied stochastic processes will also find the book useful. The author restricts himself exclusively to Markov processes with diffusions as the core of the material. Emphasis is laid on systematic approximation methods (small noise expansion, adiabatic elimination); the range of the validity of these methods is discussed. The book is carefully organized and the presentation is extremely clear. Although the book is not intended to be rigorous in the mathematical sense the results are made plausible by "demonstrations'' and illustrated by a variety of well-chosen examples. The 10 chapters can be divided into three parts. Part I consists of: 1. A historical introduction, 2. Probability concepts, 3. Markov processes. Part II is the core of the book: 4. The Itô calculus and stochastic differential equations, 5. The Fokker-Planck equation, 6. Approximation methods for diffusion processes. Part III gives applications and generalizations: 7. Master equations and jump processes, 8. Spatially distributed systems, 9. Bistability, metastability, and escape problems, 10. Quantum mechanical Markov processes. Warning: The definition of the Stratonovich stochastic integral in Sections 4.2.3 and 4.3.6 is not correct. %7 Third %@ 3-540-20882-8

@book{gardiner2004handbook, abstract = {(MR) The second edition has been reviewed [Handbook of stochastic methods, 1985; MR0858704 (87i:00033)]. This third edition includes a chapter on the numerical treatment of stochastic differential equations but the chapter on quantum Markov processes has been deleted because it had become obsolete. (For an updated treatment of this material see [C. W. Gardiner and P. Zoller, Quantum noise, Second edition, Springer, Berlin, 2000; MR1736115 (2003f:81298)].) This book fills a gap between mathematically oriented expositions of the theories of stochastic processes and stochastic differential equations on the one hand and applications to certain fields (e.g., in engineering) on the other. It provides stochastic methods nowadays frequently used in statistical and quantum physics, theoretical chemistry, and electronics. Among other things the author tries to give (and succeeds in giving) an audience of nonprobabilists insight into the seemingly inaccessible Itô calculus. The readership is intended to consist of theoretical physicists and chemists, but the reviewer is sure that engineers and mathematicians working in applied stochastic processes will also find the book useful. The author restricts himself exclusively to Markov processes with diffusions as the core of the material. Emphasis is laid on systematic approximation methods (small noise expansion, adiabatic elimination); the range of the validity of these methods is discussed. The book is carefully organized and the presentation is extremely clear. Although the book is not intended to be rigorous in the mathematical sense the results are made plausible by "demonstrations'' and illustrated by a variety of well-chosen examples. The 10 chapters can be divided into three parts. Part I consists of: 1. A historical introduction, 2. Probability concepts, 3. Markov processes. Part II is the core of the book: 4. The Itô calculus and stochastic differential equations, 5. The Fokker-Planck equation, 6. Approximation methods for diffusion processes. Part III gives applications and generalizations: 7. Master equations and jump processes, 8. Spatially distributed systems, 9. Bistability, metastability, and escape problems, 10. Quantum mechanical Markov processes. Warning: The definition of the Stratonovich stochastic integral in Sections 4.2.3 and 4.3.6 is not correct. }, added-at = {2011-02-09T00:10:33.000+0100}, address = {Berlin}, author = {Gardiner, C. W.}, biburl = {https://www.bibsonomy.org/bibtex/269765d3855041f02567cd84d931f305b/peter.ralph}, edition = {Third}, interhash = {0a57802d674483628fe9dc84ec2f6fd9}, intrahash = {69765d3855041f02567cd84d931f305b}, isbn = {3-540-20882-8}, keywords = {SDE reference}, mrclass = {00A69 (60-01 60Hxx 60Jxx 82C31)}, mrnumber = {2053476 (2004m:00008)}, pages = {xviii+415}, publisher = {Springer-Verlag}, series = {Springer Series in Synergetics}, timestamp = {2011-02-09T00:10:33.000+0100}, title = {Handbook of stochastic methods for physics, chemistry and the natural sciences}, volume = 13, year = 2004 }