Stabilization by Noise of a C-2-valued Coupled System
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.
Stochastics and Dynamics
Chen, J. P.,
(2017). Stabilization by Noise of a C-2-valued Coupled System. Stochastics and Dynamics, 17(6).
Available at: https://aquila.usm.edu/fac_pubs/17653