Work

Exact probability distribution functions for Parrondo's games

Year: 2016

Type: article

Abstract: We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.

Source: Physical review. E

DOI: 10.1103/physreve.94.060102

Authors: Rubina Zadourian, David B. Saakian, Andreas Klümper

Institutions: Max Planck Institute for the Physics of Complex Systems, A. Alikhanyan National Laboratory, Institute of Physics, Academia Sinica, University of Wuppertal

Language: English

Topic: stochastic dynamics and bifurcation

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Science and Technology, Academia Sinica

Awards: G4548501806, G6054351978