Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A review of probability theory
- 2 Differential equations
- 3 Stochastic equations with Gaussian noise
- 4 Further properties of stochastic processes
- 5 Some applications of Gaussian noise
- 6 Numerical methods for Gaussian noise
- 7 Fokker–Planck equations and reaction–diffusion systems
- 8 Jump processes
- 9 Levy processes
- 10 Modern probability theory
- Appendix A Calculating Gaussian integrals
- References
- Index
Preface
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 A review of probability theory
- 2 Differential equations
- 3 Stochastic equations with Gaussian noise
- 4 Further properties of stochastic processes
- 5 Some applications of Gaussian noise
- 6 Numerical methods for Gaussian noise
- 7 Fokker–Planck equations and reaction–diffusion systems
- 8 Jump processes
- 9 Levy processes
- 10 Modern probability theory
- Appendix A Calculating Gaussian integrals
- References
- Index
Summary
This book is intended for a one-semester graduate course on stochastic methods. It is specifically targeted at students and researchers who wish to understand and apply stochastic methods to problems in the natural sciences, and to do so without learning the technical details of measure theory. For those who want to familiarize themselves with the concepts and jargon of the “modern” measure-theoretic formulation of probability theory, these are described in the final chapter. The purpose of this final chapter is to provide the interested reader with the jargon necessary to read research articles that use the modern formalism. This can be useful even if one does not require this formalism in one's own research.
This book contains more material than I cover in my current graduate class on the subject at UMass Boston. One can select from the text various optional paths depending on the purpose of the class. For a graduate class for physics students who will be using stochastic methods in their research work, whether in physics or interdisciplinary applications, I would suggest the following: Chapters 1, 2, 3 (with Section 3.8.5 optional), 4 (with Section 4.2 optional, as alternative methods are given in 7.7), 5 (with Section 5.2 optional), 7 (with Sections 7.8 and 7.9 optional), and 8 (with Section 8.9 optional). In the above outline I have left out Chapters 6, 9 and 10.
- Type
- Chapter
- Information
- Stochastic Processes for PhysicistsUnderstanding Noisy Systems, pp. xi - xiiPublisher: Cambridge University PressPrint publication year: 2010