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Random Processes in Physics and Finance$
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Melvin Lax, Wei Cai, and Min Xu

Print publication date: 2006

Print ISBN-13: 9780198567769

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567769.001.0001

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Examples of Markovian processes

Examples of Markovian processes

Chapter:
(p.48) 3 Examples of Markovian processes
Source:
Random Processes in Physics and Finance
Author(s):

Melvin Lax

Wei Cai

Min Xu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567769.003.0003

Consider two physical problems describable by the same random process. The first process is the radioactive decay of a collection of nuclei. The second is the production of photoelectrons by a steady beam of light on a photodetector. In both cases, we can let a discrete, positive, integer valued, variable n(t) represent the number of counts emitted in the time interval between 0 and t. This is the essence of the Poisson process, an example of Markovian process. Other examples of Markovian processes include the one dimensional random walk, gambler's ruin, diffusion processes and the Einstein relation, Brownian motion, Langevin theory of velocities in Brownian motion, Langevin theory of positions in Brownian motion, and chaos.

Keywords:   Markovian processes, Poisson process, random process, random walk, gambler's ruin, diffusion processes, Einstein relation, Brownian motion, Langevin theory, chaos

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