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Infinite-Dimensional Calculus Under Weak Spatial Regularity of the Processes

Author

Listed:
  • Franco Flandoli

    (Università di Pisa)

  • Francesco Russo

    (ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques appliquées)

  • Giovanni Zanco

    (Institute of Science and Technology Austria (IST Austria))

Abstract

Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus.

Suggested Citation

  • Franco Flandoli & Francesco Russo & Giovanni Zanco, 2018. "Infinite-Dimensional Calculus Under Weak Spatial Regularity of the Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 789-826, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0724-2
    DOI: 10.1007/s10959-016-0724-2
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