Noise-induced stabilization of planar flows I
Abstract
© 2015 University of Washington. All rights reserved.We show that the complex-valued
ODE (n ≥ 1, an+1 6≠ 0): ź = an+1zn+1 + anzn +1zn + a0; which necessarily has trajectories
along which the dynamics blows up in finite time, can be stabilized by the addition
of an arbitrarily small elliptic, additive Brownian stochastic term. We also show
that the stochastic perturbation has a unique invariant probability measure which
is heavy-tailed yet is uniformly, exponentially attracting. The methods turn on the
construction of Lyapunov functions. The techniques used in the construction are general
and can likely be used in other settings where a Lyapunov function is needed. This
is a two-part paper. This paper, Part I, focuses on general Lyapunov methods as applied
to a special, simplified version of the problem. Part II [11] extends the main results
to the general setting.
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https://hdl.handle.net/10161/10770Published Version (Please cite this version)
10.1214/EJP.v20-4047Publication Info
Herzog, DP; & Mattingly, JC (2015). Noise-induced stabilization of planar flows I. Electronic Journal of Probability, 20. 10.1214/EJP.v20-4047. Retrieved from https://hdl.handle.net/10161/10770.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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