Probability and Stochastic Processes for Physicists
This book seeks to bridge the gap between the parlance, the models, and even the notations used by physicists and those used by mathematicians when it comes to the topic of probability and stochastic processes. The opening four chapters elucidate the basic concepts of probability, including probabil...
Main Author: | |
---|---|
Format: | eBook |
Language: | English |
Published: |
Cham
Springer International Publishing
2020, 2020
|
Edition: | 1st ed. 2020 |
Series: | UNITEXT for Physics
|
Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Part 1: Probability
- Chapter 1. Probability spaces
- Chapter 2. Distributions
- Chapter 3. Random variables
- Chapter 4. Limit theorems
- Part 2: Stochastic Processes
- Chapter 5. General notions
- Chapter 6. Heuristic definitions
- Chapter 7. Markovianity
- Chapter 8. An outline of stochastic calculus
- Part 3: Physical modeling
- Chapter 9. Dynamical theory of Brownian motion
- Chapter 10. Stochastic mechanics
- Part 4: Appendices
- A Consistency (Sect. 2.3.4)
- B Inequalities (Sect. 3.3.2)
- C Bertrand’s paradox (Sect. 3.5.1)
- D Lp spaces of rv’s (Sect. 4.1)
- E Moments and cumulants (Sect. 4.2.1)
- F Binomial limit theorems (Sect. 4.3)
- G Non uniform point processes (Sect 6.1.1)
- H Stochastic calculus paradoxes (Sect. 6.4.2)
- I Pseudo-Markovian processes (Sect. 7.1.2)
- J Fractional Brownian motion (Sect. 7.1.10)
- K Ornstein-Uhlenbeck equations (Sect. 7.2.4)
- L Stratonovich integral (Sect. 8.2.2)
- M Stochastic bridges (Sect. 10.2)
- N Kinematics of Gaussian diffusions (Sect. 10.3.1)
- O Substantial operators (Sect. 10.3.3)
- P Constant diffusion coefficients (Sect. 10.4)