Title

Stabilization by Noise of a C-2-valued Coupled System

Document Type

Article

Publication Date

12-2017

Department

Marine Science

Abstract

D. Herzog and J. Mattingly have shown that a C-valued polynomial ODE with finite-time blow-up solutions may be stabilized by the addition of C-valued Brownian noise. In this paper, we extend their results to a C-2-valued system of coupled ODEs with finite-time blow-up solutions. We show analytically and numerically that stabilization can be achieved in our setting by adding a suitable Brownian noise, and that the resulting system of SDEs is ergodic. The proof uses the Girsanov theorem to induce a time change from our C-2-system to a quasi-C-system similar to the one studied by Herzog and Mattingly.

Publication Title

Stochastics and Dynamics

Volume

17

Issue

6

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