Noise-induced stabilization of planar flows ii
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© 2015 University of Washington. All rights reserved.We continue the work started in Part I , 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.
Published Version (Please cite this version)10.1214/EJP.v20-4048
Publication InfoHerzog, David P; & Mattingly, Jonathan Christopher (2015). Noise-induced stabilization of planar flows ii. Electronic Journal of Probability, 20. 10.1214/EJP.v20-4048. Retrieved from https://hdl.handle.net/10161/9512.
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James B. Duke Professor
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and