An Oscillator Driven by Algebraically Decorrelating Noise

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...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 402; no. 1; pp. 231 - 284
Main Authors Gomez, Chistophe, Iyer, Gautam, Le, Hai, Novikov, Alexei
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2023
Springer Nature B.V
Springer Verlag
Subjects
Brownian motion
Classical and Quantum Gravitation
Complex Systems
Convergence
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Oscillators
Physics
Physics and Astronomy
Quantum Physics
Random noise
Relativity Theory
Theoretical
Diffusion-approximation
Hamiltonian systems
Random perturbations
Algebraic decaying correlations
Fractional processes
60H10
60G15 Hamiltonian systems
2010 Mathematics Subject Classification. Primary 37H05
Secondary 60F05
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-023-04744-3