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Brownian MotionFluctuations, Dynamics, and Applications$
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Robert M. Mazo

Print publication date: 2008

Print ISBN-13: 9780199556441

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199556441.001.0001

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Brownian Motion

Robert M. Mazo

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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