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The fractional stochastic heat equation on the circle: Time regularity and potential theory

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  • Nualart, Eulalia
  • Viens, Frederi

Abstract

We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S1. We obtain sharp results on the Hölder continuity in time of the paths of the solution . We then establish upper and lower bounds on hitting probabilities of u, in terms of the Hausdorff measure and Newtonian capacity respectively.

Suggested Citation

  • Nualart, Eulalia & Viens, Frederi, 2009. "The fractional stochastic heat equation on the circle: Time regularity and potential theory," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1505-1540, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1505-1540
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    References listed on IDEAS

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    1. Quer-Sardanyons, Lluís & Tindel, Samy, 2007. "The 1-d stochastic wave equation driven by a fractional Brownian sheet," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1448-1472, October.
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    Cited by:

    1. Wei Liu & Kuanhou Tian & Mohammud Foondun, 2017. "On Some Properties of a Class of Fractional Stochastic Heat Equations," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1310-1333, December.
    2. Balan, Raluca M. & Tudor, Ciprian A., 2010. "The stochastic wave equation with fractional noise: A random field approach," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2468-2494, December.

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