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Stochastic differential equation derivation: Comparison of the Markov method versus the additive method

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  • Galayda, S.
  • Barany, E.

Abstract

There are several methods of transforming an ordinary differential equation into a stochastic differential equation (SDE). The two most common are adding noise to a system parameter or variable and transforming to a SDE or deriving the SDE by assuming an underlying Markov process. Using simple one- and two-dimensional systems we investigate the differences in dynamics and bifurcations between SDE derived by each method from simple deterministic population models.

Suggested Citation

  • Galayda, S. & Barany, E., 2012. "Stochastic differential equation derivation: Comparison of the Markov method versus the additive method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4564-4574.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4564-4574
    DOI: 10.1016/j.physa.2012.05.028
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    References listed on IDEAS

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    1. IonuĊ£ Florescu & Maria Cristina Mariani & Granville Sewell, 2011. "Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1445-1452, August.
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    Cited by:

    1. Vaidya, Tushar & Chotibut, Thiparat & Piliouras, Georgios, 2021. "Broken detailed balance and non-equilibrium dynamics in noisy social learning models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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