Stochastic Tools in Mathematics and Science

1. Front Matter

   Pages i-xi

   PDF

2. Preliminaries

   • Alexandre J. Chorin, Ole H. Hald

   Pages 1-23

3. Introduction to Probability

   • Alexandre J. Chorin, Ole H. Hald

   Pages 25-45

4. Computing with Probability

   • Alexandre J. Chorin, Ole H. Hald

   Pages 47-62

5. Brownian Motion with Applications

   • Alexandre J. Chorin, Ole H. Hald

   Pages 63-88

6. Time-Varying Probabilities

   • Alexandre J. Chorin, Ole H. Hald

   Pages 89-107

7. Stationary Stochastic Processes

   • Alexandre J. Chorin, Ole H. Hald

   Pages 109-132

8. Statistical Mechanics

   • Alexandre J. Chorin, Ole H. Hald

   Pages 133-155

9. Computational Statistical Mechanics

   • Alexandre J. Chorin, Ole H. Hald

   Pages 157-170

10. Generalized Langevin Equations

    • Alexandre J. Chorin, Ole H. Hald

    Pages 171-198

11. Erratum to: Chapter 9 Generalized Langevin Equations

    • Alexandre J. Chorin, Ole H. Hald

    Pages E1-E1

12. Back Matter

    Pages 199-200

    PDF

"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises. Review of earlier edition: "This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science." Mathematical Reviews, 2006

• Brownian Motion
• Least Squares Approximation
• Monte Carlo Methods
• Stationary Stochastic Processes
• Statistical Mechanics
• Time-Dependent Statistical Mechanics

• University of California, Berkeley Dept. Mathematics, Berkeley, USA

  Alexandre J. Chorin

• Department of Mathematics University of California at Berkeley, Berkeley, USA

  Ole H Hald

Alexandre J. Chorin is a professor of mathematics at the University of California, Berkeley who works in applied mathematics. He is known for his contributions to the field of Computational fluid dynamics. Ole Hald is a professor of mathematics at the University of California, Berkeley.

Policies and ethics