- Title Pages
- International Series of Monographs on Physics
- Preface
- 1 HISTORICAL BACKGROUND
- 2 PROBABILITY THEORY
- 3 STOCHASTIC PROCESSES
- 4 EINSTEIN–SMOLUCHOWSKI THEORY
- 5 STOCHASTIC DIFFERENTIAL EQUATIONS AND INTEGRALS
- 6 FUNCTIONAL INTEGRALS
- 7 SOME IMPORTANT SPECIAL CASES
- 8 THE SMOLUCHOWSKI EQUATION
- 9 RANDOM WALK
- 10 STATISTICAL MECHANICS
- 11 STOCHASTIC EQUATIONS FROM A STATISTICAL MECHANICAL VIEWPOINT
- 12 TWO EXACTLY TREATABLE MODELS
- 13 BROWNIAN MOTION AND NOISE
- 14 DIFFUSION PHENOMENA
- 15 ROTATIONAL DIFFUSION
- 16 POLYMER SOLUTIONS
- 17 INTERACTING BROWNIAN PARTICLES
- 18 DYNAMICS, FRACTALS, AND CHAOS
- Appendix A The Applicability of Stokes’ Law
- Appendix B Functional Calculus
- Appendix C An Operator Identity
- Appendix D Euler Angles
- Appendix E The Oseen Tensor
- Appendix F Mutual Diffusion and Self-Diffusion
- References
- Index
STOCHASTIC PROCESSES
STOCHASTIC PROCESSES
- Chapter:
- (p.26) 3 STOCHASTIC PROCESSES
- Source:
- Brownian Motion
- Author(s):
Robert M. Mazo
- Publisher:
- Oxford University Press
This chapter extends the ideas of Chapter 2 by introducing the notion of stochastic process or random process and its distribution functions. The idea of a Markov process is defined. The Chapman–Kolmagorov equation for Markov processes is given. From this, the Fokker–Planck equation for homogeneous continuous Markov processes is derived. The calculus of stochastic processes is then discussed, i.e., questions of what is meant by convergence, continuity, integration, Fourier analysis. The chapter concludes with a short discussion of white noise, a completely random process.
Keywords: stochastic process, random process, Markov process, Chapman–Kolmogorov equation, Fokker–Planck, white noise
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- Title Pages
- International Series of Monographs on Physics
- Preface
- 1 HISTORICAL BACKGROUND
- 2 PROBABILITY THEORY
- 3 STOCHASTIC PROCESSES
- 4 EINSTEIN–SMOLUCHOWSKI THEORY
- 5 STOCHASTIC DIFFERENTIAL EQUATIONS AND INTEGRALS
- 6 FUNCTIONAL INTEGRALS
- 7 SOME IMPORTANT SPECIAL CASES
- 8 THE SMOLUCHOWSKI EQUATION
- 9 RANDOM WALK
- 10 STATISTICAL MECHANICS
- 11 STOCHASTIC EQUATIONS FROM A STATISTICAL MECHANICAL VIEWPOINT
- 12 TWO EXACTLY TREATABLE MODELS
- 13 BROWNIAN MOTION AND NOISE
- 14 DIFFUSION PHENOMENA
- 15 ROTATIONAL DIFFUSION
- 16 POLYMER SOLUTIONS
- 17 INTERACTING BROWNIAN PARTICLES
- 18 DYNAMICS, FRACTALS, AND CHAOS
- Appendix A The Applicability of Stokes’ Law
- Appendix B Functional Calculus
- Appendix C An Operator Identity
- Appendix D Euler Angles
- Appendix E The Oseen Tensor
- Appendix F Mutual Diffusion and Self-Diffusion
- References
- Index
