Noise-induced stabilization of planar flows ii


Journal Article

© 2015 University of Washington. All rights reserved. We continue the work started in Part I [6], 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 [7] generalized Tanaka formula adapted to patching together Lyapunov functions. This greatly simplifies the analysis used in previous works.

Full Text

Duke Authors

Cited Authors

  • Herzog, DP; Mattingly, JC

Published Date

  • October 25, 2015

Published In

Volume / Issue

  • 20 /

Electronic International Standard Serial Number (EISSN)

  • 1083-6489

Digital Object Identifier (DOI)

  • 10.1214/EJP.v20-4048

Citation Source

  • Scopus