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Additive Functionals of the Solution to Fractional Stochastic Heat Equation

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Abstract

We give sharp regularity results for the solution to the linear stochastic heat equation with fractional noise in time. We apply these result to prove the local nondeterminism of this process and to study the existence and the joint continuity of its local times.

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Acknowledgement

The second author is grateful to Professors Antoine Ayache and Yimin Xiao for useful discussions.

Author information

Authors and Affiliations

  1. Faculty of Sciences, Université Mohammed 1, Box 717, Oujda, Morocco

    Hanae Ouahhabi

  2. Laboratoire Paul Painlevé, Université de Lille 1, 59655, Villeneuve d’Ascq, France

    Ciprian A. Tudor

  3. Academy of Economical Studies, Piata Romana nr. 6, sector 1, Bucharest, Romania

    Ciprian A. Tudor

Authors
  1. Hanae Ouahhabi
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  2. Ciprian A. Tudor
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Corresponding author

Correspondence to Ciprian A. Tudor.

Additional information

Communicated by Stéphane Jaffard.

C.A. Tudor was supported by the CNCS grant PN-II-ID-PCCE-2011-2-0015 (Romania). Associate member of the team Samm, Université de Panthéon-Sorbonne Paris 1. The author also acknowledges partial support from ANR “Masterie” BLANC 012103 (France).

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Ouahhabi, H., Tudor, C.A. Additive Functionals of the Solution to Fractional Stochastic Heat Equation. J Fourier Anal Appl 19, 777–791 (2013). https://doi.org/10.1007/s00041-013-9272-7

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  • DOI: https://doi.org/10.1007/s00041-013-9272-7

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