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Sample path large deviations for super-Brownian motion
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  • Published: September 1996

Sample path large deviations for super-Brownian motion

  • A. Schied1 

Probability Theory and Related Fields volume 104, pages 319–347 (1996)Cite this article

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Summary

We derive two large deviation principles of Freidlin-Wentzell type for rescaled super-Brownian motion. For one of the appearing rate functions an integral representation is given and interpreted as ‘Kakutani-Hellinger energy’. As a tool we develop estimates for the Laplace functionals of (historical) super-Brownian motion and certain maximal inequalities. Also it is shown that the Hölder norm of index α<1/2 of the processt↦〈f, X t 〉 possesses some finite exponential moments provided the functionf is smooth.

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Authors and Affiliations

  1. Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, D-10099, Berlin, Germany

    A. Schied

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  1. A. Schied
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Additional information

This work was supported in part by the Graduiertenkolleg “Algebraische, analytische und geometrische Methoden und ihre Wechselwirkung in der modernen Mathematik”, Bonn

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Schied, A. Sample path large deviations for super-Brownian motion. Probab. Th. Rel. Fields 104, 319–347 (1996). https://doi.org/10.1007/BF01213684

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  • Received: 30 December 1994

  • Revised: 18 September 1995

  • Issue Date: September 1996

  • DOI: https://doi.org/10.1007/BF01213684

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Mathematics Subject Classification (1991)

  • 60J80
  • 60F10
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