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Transactions of the American Mathematical Society

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Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces


Authors: Giuseppe Da Prato, Alessandra Lunardi and Luciano Tubaro
Journal: Trans. Amer. Math. Soc. 370 (2018), 5795-5842
MSC (2010): Primary 28C20, 60H15, 35R15
DOI: https://doi.org/10.1090/tran/7195
Published electronically: April 4, 2018
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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.


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Additional Information

Giuseppe Da Prato
Affiliation: Scuola Normale Superiore Piazza dei Cavalieri, 7 56126 Pisa, Italy
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
Email: alessandra.lunardi@unipr.it

Luciano Tubaro
Affiliation: Dipartimento di Matematica Università di Trento Via Sommarive 14 38123 Povo, Italy
Email: tubaro@science.unitn.it

DOI: https://doi.org/10.1090/tran/7195
Keywords: Infinite dimensional analysis, probability measures in Hilbert spaces, surface integrals in Hilbert spaces, invariant measures, stochastic PDEs.
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”.
Article copyright: © Copyright 2018 American Mathematical Society

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