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Noise can create periodic behavior and stabilize nonlinear diffusions

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  • Scheutzow, Michael

Abstract

It is shown that unlike nondegenerate (linear) diffusion processes, nonlinear diffusion processes can have a periodic law. We provide an example of a nonlinear diffusion for which periodic behavior is even created by the noise, i.e. no periodicity occurs when the noise is turned off. In the second part of the paper we give an example of a one-dimensional nonlinear diffusion which can be stabilized by noise. Finally we show also that the N-dimensional (N >= 2) 'linear' diffusion approximations of that system are stabilized by noise.

Suggested Citation

  • Scheutzow, Michael, 1985. "Noise can create periodic behavior and stabilize nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 323-331, September.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:2:p:323-331
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    Cited by:

    1. Harin, Alexander, 2019. "Forbidden zones for the expectations of measurement data and problems of behavioral economics," MPRA Paper 91368, University Library of Munich, Germany.
    2. Ditlevsen, Susanne & Löcherbach, Eva, 2017. "Multi-class oscillating systems of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1840-1869.
    3. Alexander Harin, 2022. "Forbidden Zones for the Expectations of Data: New Mathematical Methods and Models for Behavioral Economics," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 8(1), pages 12-26, 12-2021.
    4. Harin, Alexander, 2020. "Behavioral sciences and auto-transformations of functions," MPRA Paper 99286, University Library of Munich, Germany.
    5. Alexander Harin, 2021. "Auto-Transformations of the Probability Density Functions," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 7(3), pages 167-178, 07-2021.
    6. Harin, Alexander, 2018. "Forbidden zones for the expectation. New mathematical results for behavioral and social sciences," MPRA Paper 86650, University Library of Munich, Germany.
    7. Harin, Alexander, 2018. "Inequalities and zones. New mathematical results for behavioral and social sciences," MPRA Paper 90326, University Library of Munich, Germany.
    8. Harin, Alexander, 2021. "Behavioral economics. Forbidden zones. New method and models," MPRA Paper 106545, University Library of Munich, Germany.
    9. Harin, Alexander, 2019. "Behavioral sciences and auto-transformations. Introduction," MPRA Paper 97344, University Library of Munich, Germany.

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