Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/28442
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Type: Conference paper
Title: Discrete games of chance as models for continuous stochastic transport processes
Author: Allison, A.
Abbott, D.
Citation: Noise in Complex Systems and Stochastic Dynamics, Lutz Schimansky-Geier, Derek Abbott, Alexander Neiman, Christian Van den Broeck (eds.), pp. 363-371
Publisher: SPIE
Publisher Place: Washington, USA
Issue Date: 2003
Series/Report no.: Proceedings of SPIE--the International Society for Optical Engineering ; 5114.
ISBN: 0-8194-4974-1
ISSN: 0277-786X
1996-756X
Conference Name: Noise in Complex Systems and Stochastic Dynamics (2003 : Santa Fe, New Mexico)
Editor: Jaenisch, H.M.
Handley, J.W.
Statement of
Responsibility: 
Andrew G. Allison and Derek Abbott
Abstract: Discrete games of chance can be used to illustrate principles of stochastic processes. For example, most readers are familiar with the use of discrete random walks to model the microscopic phenomenon of Brownian motion. We show that discrete games of chance, such as those of Parrondo and Astumian, can be used to quantitatively model stochastic transport processes. Discrete games can be used as "toy" models for pedagogic purposes but they can be much more than "toys". In principle we could perform accurate simulations and we could reduce the errors of approximation to any desired level, provided that we were prepared to pay the computational cost. We consider some different approaches to discrete games, in the literature, and we use partial differential equations to model the particle densities inside a Brownian Ratchet. We apply a finite difference approach and obtain finite difference equations, which are equivalent to the games of Parrondo. The new games generalize Parrondo's original games, in the context of stochastic transport problems. We provide a practical method for constructing sets of discrete games, which can be used to simulate stochastic transport processes. We also attempt to place discrete games, such as those of Parrondo and Astumian, on a more sound philosophical basis.
Description: © 2003 COPYRIGHT SPIE--The International Society for Optical Engineering
DOI: 10.1117/12.501497
Published version: http://dx.doi.org/10.1117/12.501497
Appears in Collections:Aurora harvest 2
Electrical and Electronic Engineering publications

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