Mathematical Notes
eBook - PDF

Mathematical Notes

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Mathematical Notes

Book details
Table of contents
Citations

About This Book

These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.

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Information

Publisher
Princeton University Press
Year
2020
ISBN
9780691219615
Topic
Mathematics
Subtopic
Probability & Statistics
Index
Mathematics

Table of contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. § 1. Apology
  6. § 2. Robert Brown
  7. § 3. The period before Einstein
  8. § 4. Albert Einstein
  9. § 5. Derivation of the Wiener process
  10. § 6. Gaussian processes
  11. § 7. The Wiener integral
  12. § 8. A class of stochastic differential equations
  13. § 9. The Qrnstein-Uhlenbeck theory of Brownian motion
  14. §10. Brownian motion in a force field
  15. §11. Kinematics of stochastic motion
  16. §12. Dynamics of stochastic motion
  17. §13. Kinematics of Markoffian motion
  18. §14. Remarks on quantum mechanics
  19. §15. Brownian motion in the aether
  20. §l6. Comparison with quantum mechanics