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2D-Stochastic Currents over the Wiener Sheet

Author

Listed:
  • Franco Flandoli

    (Universita di Pisa)

  • Peter Imkeller

    (Humboldt-Universität zu Berlin)

  • Ciprian A. Tudor

    (Université de Lille 1
    Academy of Economical Studies)

Abstract

By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener–Itô integrals, we define a 2D-stochastic current over the Brownian sheet. This concept comes from geometric measure theory. We also study the regularity of the stochastic current with respect to the randomness in the Watanabe spaces and with respect to the spatial variable in the deterministic Sobolev spaces.

Suggested Citation

  • Franco Flandoli & Peter Imkeller & Ciprian A. Tudor, 2014. "2D-Stochastic Currents over the Wiener Sheet," Journal of Theoretical Probability, Springer, vol. 27(2), pages 552-575, June.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:2:d:10.1007_s10959-012-0453-0
    DOI: 10.1007/s10959-012-0453-0
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    References listed on IDEAS

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    1. Coutin, Laure & Nualart, David & Tudor, Ciprian A., 2001. "Tanaka formula for the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 301-315, August.
    2. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
    Full references (including those not matched with items on IDEAS)

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