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Stochastic stabilization and destabilization

Mao, Xuerong (1994) Stochastic stabilization and destabilization. Systems and Control Letters, 23 (4). pp. 279-290. ISSN 0167-6911

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It is shown in this paper that any nonlinear systems dot x(t) = f(x(t), t) in Rd can be stabilized by Brownian motion provided |f{hook}(x,t)| ≤ K|x| for some K > 0. On the other hand, this system can also be destabilized by Brownian motion if the dimension d ≥ 2. Similar results are also obtained for any given stochastic differential equation dx(t) = f{hook}(x(t), t) + g(x(t), t) dW(t).