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The 1-d stochastic wave equation driven by a fractional Brownian sheet

Author

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  • Quer-Sardanyons, Lluís
  • Tindel, Samy

Abstract

In this paper, we develop a Young integration theory in dimension 2 which will allow us to solve a non-linear one- dimensional wave equation driven by an arbitrary signal whose rectangular increments satisfy some Hölder regularity conditions, for some Hölder exponent greater than 1/2. This result will be applied to the fractional Brownian sheet.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:10:p:1448-1472
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    Citations

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    Cited by:

    1. Jorge A. León & Samy Tindel, 2012. "Malliavin Calculus for Fractional Delay Equations," Journal of Theoretical Probability, Springer, vol. 25(3), pages 854-889, September.
    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.
    3. Zhang, Yinghan & Yang, Xiaoyuan, 2015. "Fractional stochastic Volterra equation perturbed by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 20-36.
    4. Quer-Sardanyons, Lluís & Tindel, Samy, 2012. "Pathwise definition of second-order SDEs," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 466-497.
    5. Deya, Aurélien & Tindel, Samy, 2011. "Rough Volterra equations 2: Convolutional generalized integrals," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1864-1899, August.
    6. 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.

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