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Small Noise Asymptotic of the Timing Jitter in Soliton Transmission

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  • Arnaud Debussche

    (Crest)

  • Eric Gautier

    (Crest)

Abstract

Exit from a neighborhood of zero for weakly damped stochasticnonlinear SchrÄodinger equations is studied. The small noise is either complexand of additive type or real and of multiplicative type. It is white in time andcolored in space. The neighborhood is either in L2 or in H1. The small noiseasymptotic of both the ¯rst exit times and the exit points are characterized.

Suggested Citation

  • Arnaud Debussche & Eric Gautier, 2005. "Small Noise Asymptotic of the Timing Jitter in Soliton Transmission," Working Papers 2005-20, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-20
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    File URL: http://crest.science/RePEc/wpstorage/2005-20.pdf
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    References listed on IDEAS

    as
    1. Rasmussen, K.Ø. & Gaididei, Yu.B. & Bang, O. & Christiansen, P.L., 1996. "Nonlinear and stochastic modelling of energy transfer in Scheibe aggregates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 40(3), pages 339-358.
    2. Eric Gautier, 2005. "Exit from a Neighborhood of Zero for Weakly Damped Stochastic Nonlinear Schrödinger Equations," Working Papers 2005-21, Center for Research in Economics and Statistics.
    3. C. Brunhuber & F. Mertens & Y. Gaididei, 2004. "Thermal diffusion of envelope solitons on anharmonic atomic chains," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 42(1), pages 103-112, November.
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    Cited by:

    1. Eric Gautier, 2005. "Exit from a Neighborhood of Zero for Weakly Damped Stochastic Nonlinear Schrödinger Equations," Working Papers 2005-21, Center for Research in Economics and Statistics.
    2. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.

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    1. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.

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