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First Steps in Random WalksFrom Tools to Applications$
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J. Klafter and I. M. Sokolov

Print publication date: 2011

Print ISBN-13: 9780199234868

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199234868.001.0001

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Master equations

Master equations

(p.68) 5 Master equations
First Steps in Random Walks

J. Klafter

I.M. Sokolov

Oxford University Press

The probabilistic approaches outlined above rely on assumptions of homogeneity of the motion in space and in time allowing for using the Fourier‐Laplace representation. These assumptions can be released when turning to master equations giving probabilities to find a walker at a given position. The chapter discusses generalized master equations and their customary version (the ones for exponential waiting time distributions). It shows the relations between the solutions of generalized and customary master equations, and discuss their space‐continuous versions, the (generalized) Fokker‐Planck and diffusion equations.

Keywords:   master equation, generalized Master equation, time‐dependent transition probabilities, subordination, Einstein's relation

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