We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.
Valenti, D., Chichigina, O., Dubkov, A., Spagnolo, B. (2015). Stochastic acceleration in generalized squared Bessel processes. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2015(2), P02012-1-P02012-16 [10.1088/1742-5468/2015/02/P02012].
Stochastic acceleration in generalized squared Bessel processes
VALENTI, Davide
;SPAGNOLO, Bernardo
2015-01-01
Abstract
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.File | Dimensione | Formato | |
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