Electronic Journal of Probability

Noise-induced stabilization of planar flows II

David Herzog and Jonathan Mattingly

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We continue the work started in Part I of this article, showing how the addition of noise can stabilize an otherwise unstable system. The analysis makes use of nearly optimal Lyapunov functions. In this continuation, we remove the main limiting assumption of Part I by an inductive procedure as well as establish a lower bound which shows that our construction is radially sharp. We also prove a version of Peskir's  generalized Tanaka formula adapted to patching together Lyapunov functions. This greatly simplifies the analysis used in previous works.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 113, 37 pp.

Accepted: 25 October 2015
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 37B25: Lyapunov functions and stability; attractors, repellers

Noise-induced stabilization Lyapunov functions

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Herzog, David; Mattingly, Jonathan. Noise-induced stabilization of planar flows II. Electron. J. Probab. 20 (2015), paper no. 113, 37 pp. doi:10.1214/EJP.v20-4048. https://projecteuclid.org/euclid.ejp/1465067219

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See also

  • David Herzog, Jonathan Mattingly. Noise-induced stabilization of planar flows I.