An Oscillator Driven by Algebraically Decorrelating Noise

• Published in: Communications in mathematical physics Vol. 402; no. 1; pp. 231 - 284
• Main Authors: Gomez, Chistophe, Iyer, Gautam, Le, Hai, Novikov, Alexei
• Format: Journal Article
• Language: English
• 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
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-023-04744-3

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...