Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces
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- by Giuseppe Da Prato, Alessandra Lunardi and Luciano Tubaro PDF
- Trans. Amer. Math. Soc. 370 (2018), 5795-5842 Request permission
Abstract:
We construct surface measures in a Hilbert space endowed with a probability measure $\nu$. The theory fits for invariant measures of some stochastic partial differential equations such as Burgers and reaction–diffusion equations. Other examples are weighted Gaussian measures and special product measures $\nu$ of non-Gaussian measures. In any case we prove integration by parts formulae on sublevel sets of good functions (including spheres and hyperplanes) that involve surface integrals.References
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Additional Information
- Giuseppe Da Prato
- Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
- MR Author ID: 53850
- Email: g.daprato@sns.it
- Alessandra Lunardi
- Affiliation: Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze, 53/A, 43124 Parma, Italy
- MR Author ID: 116935
- Email: alessandra.lunardi@unipr.it
- Luciano Tubaro
- Affiliation: Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo, Italy
- MR Author ID: 175055
- Email: tubaro@science.unitn.it
- Received by editor(s): August 20, 2016
- Received by editor(s) in revised form: December 6, 2016, and January 8, 2017
- Published electronically: April 4, 2018
- Additional Notes: This work was partially supported by the research project PRIN 2010MXMAJR “Evolution differential problems: deterministic and stochastic approaches and their interactions”.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 5795-5842
- MSC (2010): Primary 28C20, 60H15, 35R15
- DOI: https://doi.org/10.1090/tran/7195
- MathSciNet review: 3803148