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...

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Bibliographic Details
Main Author: Cufaro Petroni, Nicola
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)