Share Email Print

Proceedings Paper

Discrete games of chance as models for continuous stochastic transport processes
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper 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.

Paper Details

Date Published: 7 May 2003
PDF: 9 pages
Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); doi: 10.1117/12.501497
Show Author Affiliations
Andrew G. Allison, The Univ. of Adelaide (Australia)
Derek Abbott, The Univ. of Adelaide (Australia)

Published in SPIE Proceedings Vol. 5114:
Noise in Complex Systems and Stochastic Dynamics
Lutz Schimansky-Geier; Derek Abbott; Alexander Neiman; Christian Van den Broeck, Editor(s)

© SPIE. Terms of Use
Back to Top
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?