Minimal Noise-Induced Stabilization of One-Dimensional Diffusions

Tony Allen, West Virginia University
Emily Gebhardt, Mercyhurst University
Adam Kluball, Bethany Lutheran College
Tiffany 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.