Differential calculus for Dirichlet forms : the measure-valued gradient preserved by image

Article, Preprint English OPEN
Bouleau, Nicolas;
  • Publisher: Elsevier
  • Journal: Journal of Functional Analysis,volume 225,issue 1,pages63-73 (issn: 0022-1236)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1016/j.jfa.2005.02.010
  • Subject: [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR] | differential calculus | MSC 31C25 65G99 60H07 | error calculus | gradient | Mathematics - Probability | 31C25 65G99 60H07 | Analysis | Dirichlet form | Gaussian measure

In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\Gamma$ which is linear and with a good be... View more
  • References (8)

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    [3] Bouleau, N. Error Calculus for Finance and Physics, the Language of Dirichlet Forms, De Gruyter 2003.

    [4] Bouleau, N. and Hirsch, F. Dirichlet forms and analysis on Wiener space, de Gruyter 1991.

    [5] Feyel, D. and de la Pradelle, A. “Espaces de Sobolev gaussiens” Ann. Inst. Fourier 39-4, 875-908, 1989.

    [6] Ma, Z. M. and Ro¨ckner, M., Introduction to the theory of (non symmetric) Dirichlet forms, Springer 1991.

    [7] Malliavin, P. Stochastic Analysis, Springer 1997.

    [8] Nualart, D. The Malliavin Calculus and related Topics, Springer 1995.

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