Noise-induced stabilization of planar flows ii
Abstract
© 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.
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Journal articlePermalink
https://hdl.handle.net/10161/9512Published Version (Please cite this version)
10.1214/EJP.v20-4048Publication Info
(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.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Jonathan Christopher Mattingly
James B. Duke Distinguished 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
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