A Paradox in the Langevin Equation with Long-Time Noise Correlations
Abstract
We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not stabilizes but diminishes with time. It is shown that algebraic distributions can induce such non-stationary affects. Results are compared to those obtained with a deterministic random force. Consequences for the diffusion process are also discussed.
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