Exact ratchet description of Parrondo's games with self-transitions

Pau Amengual; Raul Toral

doi:10.1117/12.556418

25 May 2004 Exact ratchet description of Parrondo's games with self-transitions

Pau Amengual, Raul Toral

Proceedings Volume 5471, Noise in Complex Systems and Stochastic Dynamics II; (2004) https://doi.org/10.1117/12.556418
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain

Abstract

We extend a recently developed relation between the master equation describing the Parrondo's games and the formalism of the Fokker-Planck equation to the case in which the games are modified with the introduction of "self-transition probabilities." This accounts for the possibility that the capital can neither increase nor decrease during a game. Using this exact relation, we obtain expressions for the stationary probability and current (games gain) in terms of an effective potential. We also demonstrate that the expressions obtained are nothing but a discretised version of the equivalent expressions in terms of the solution of the Fokker-Planck equation with multiplicative noise.

Citation Download Citation

Pau Amengual and Raul Toral "Exact ratchet description of Parrondo's games with self-transitions", Proc. SPIE 5471, Noise in Complex Systems and Stochastic Dynamics II, (25 May 2004); https://doi.org/10.1117/12.556418

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