Surface integrals in Hilbert spaces for general measures and applications
Surface integrals in a Hilbert space are useful tools in stochastic analysis, including in the author's recent studies on Dirichlet problems in Hilbert space [with \textit{A. Lunardi}, J. Funct. Anal. 259, No. 10, 2642--2672 (2010; Zbl 1204.35172); J. Math. Pures Appl. (9) 99, No. 6, 741--765 (2013; Zbl 1293.35359)] and Neumann problems [with \textit{A. Lunardi}, Ann. Inst. Henri Poincaré, Probab. Stat. 51, No. 3, 1102--1123 (2015; Zbl 1330.35514)]. In this paper, the author presents a construction of a surface measure under a local Malliavin condition. Also, integration by parts formulas and some examples are given. The \(I_1\) in the last displayed equation in Example 3.8 may be a misprint of \(I_2\). For the entire collection see [Zbl 1386.70002].
scientific article; zbMATH DE number 6856133