Volume 96, Number 5, December 2011
|Number of page(s)||6|
|Published online||24 November 2011|
Non-Gaussian fluctuations in stochastic models with absorbing barriers
Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze - Via di Santa Marta 3, 50139 Firenze, Italy, EU
2 Dipartimento di Fisica, Sapienza Università di Roma - P.le A. Moro 2, 00185 Roma, Italy, EU
3 Dipartimento di Energetica, Università degli Studi di Firenze and CNISM - Via di Santa Marta 3, 50139 Firenze, Italy, EU
4 Centro Interdipartimentale per lo Studio delle Dinamiche Complesse - Via Sansone 1, 50019 Sesto Fiorentino, Italy, EU
5 INFN Sezione di Firenze - Via Sansone 1, 50019 Sesto Fiorentino, Italy, EU
Accepted: 22 October 2011
The dynamics of a one-dimensional stochastic model is studied in the presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher-order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non-Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for all times and arbitrarily close to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2011
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