Abstract
Correlation functions and correlation times for the Stratonovich and Verhulst model are investigated. By transforming the Fourier transform of the corresponding Fokker-Planck equation into a tridiagonal vector recurrence relation, the Fourier transform of the correlation function and the correlation time are expressed in terms of matrix continued fractions or by similar iterations and are thus obtained numerically. By using the inverse Fourier transform, the correlation function itself is calculated. Furthermore an analytic expression in terms of an integral is obtained for the correlation time, which is evaluated exactly in the Verhulst model and asymptotically for large and weak noise strength in the Stratonovich model. A Padé expansion approximating the correlation time for all noise strength is also given.
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Jung, P., Risken, H. Correlation functions and correlation times for models with multiplicative white noise. Z. Physik B - Condensed Matter 59, 469–481 (1985). https://doi.org/10.1007/BF01328860
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DOI: https://doi.org/10.1007/BF01328860