Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 113, 37 pp.
Noise-induced stabilization of planar flows II
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.
Electron. J. Probab., Volume 20 (2015), paper no. 113, 37 pp.
Accepted: 25 October 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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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
- David Herzog, Jonathan Mattingly. Noise-induced stabilization of planar flows I.