In this paper, we consider the sets Kr={g≥r} defined in an infinite-dimensional Hilbert space, where g is suitably related to a reference Gaussian measure μ in H. We first show how to define a surface measure that is related to μ. This allows to introduce an integration-by-parts formula in Kr, which can be applied in several important constructions, as is the case where μ is the law of a (Gaussian) stochastic process and H is the space of its trajectories.
Construction of a surface integral under local Malliavin assumptions, and related integration by parts formulas / Bonaccorsi, Stefano; Da Prato, Giuseppe; Tubaro, Luciano. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - STAMPA. - 2018, 18:2(2018), pp. 871-897. [10.1007/s00028-017-0423-1]
Construction of a surface integral under local Malliavin assumptions, and related integration by parts formulas
Bonaccorsi, Stefano;Da Prato, Giuseppe;Tubaro, Luciano
2018-01-01
Abstract
In this paper, we consider the sets Kr={g≥r} defined in an infinite-dimensional Hilbert space, where g is suitably related to a reference Gaussian measure μ in H. We first show how to define a surface measure that is related to μ. This allows to introduce an integration-by-parts formula in Kr, which can be applied in several important constructions, as is the case where μ is the law of a (Gaussian) stochastic process and H is the space of its trajectories.File | Dimensione | Formato | |
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