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Minimal Noise-Induced Stabilization of One-Dimensional Diffusions
The Minnesota Journal of Undergraduate Mathematics (2017)
  • Tony Allen, West Virginia University
  • Emily Gebhardt, Mercyhurst University
  • Adam Kluball, Bethany Lutheran College
  • Tiffany N Kolba, Valparaiso University
The phenomenon of noise-induced stabilization occurs when an unstable deterministic system of ordinary differential equations is stabilized by the addition of randomness into the system. In this paper, we investigate under what conditions one-dimensional, autonomous stochastic differential equations are stable, where we take the notion of stability to be that of global stochastic boundedness. Specifically, we find the minimum amount of noise necessary for noise-induced stabilization to occur when the drift and noise coefficients are power, polynomial, exponential, or logarithmic functions.
Publication Date
July 17, 2017
Citation Information
Tony Allen, Emily Gebhardt, Adam Kluball and Tiffany N Kolba. "Minimal Noise-Induced Stabilization of One-Dimensional Diffusions" The Minnesota Journal of Undergraduate Mathematics Vol. 3 Iss. 1 (2017) ISSN: 2378-5810
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