Publication 21-CNA-007

An Oscillator Driven By Algebraically Decorrelating Noise

Chistophe Gomez
Aix Marseille Univ, CNRS, I2M
Marseille, France
christophe.gomez@univ-amu.fr

Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
gautam@math.cmu.edu

Hai Le
Department of Mathematics
Pennsylvania State University
State College PA 16802
hvl2@psu.edu

Alexei Novikov
Department of Mathematics
Pennsylvania State University
State College PA 16802
anovikov@math.psu.edu

Abstract: We consider a stochastically forced nonlinear oscillator driven by a stationary Gaussian noise that has an algebraically decaying covariance function. It is well known that such noise processes can be renormalized to converge to fractional Brownian motion, a process that has memory. In contrast, we show that the renormalized limit of the nonlinear oscillator driven by this noise converges to diffusion driven by standard (not fractional) Brownian motion, and thus retains no memory in the scaling limit. The proof is based on the study of a fast-slow system using the perturbed test function method.

Get the paper in its entirety as  21-CNA-007.pdf

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