Malliavin calculus for regularity structures: The case of gPAM

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• 作者：G. Cannizzaro^a ; P.K. Friz^a ; ^b ; ^{friz@math.tu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; P. Gassiat^c
• 关键词：Regularity structures ; Malliavin calculus ; Generalized parabolic Anderson model ; Singular SPDEs
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：272
• 期：1
• 页码：363-419
• 全文大小：933 K

文摘

Malliavin calculus is implemented in the context of Hairer (2014) [16]. This involves some constructions of independent interest, notably an extension of the structure which accommodates a robust, and purely deterministic, translation operator, in L²$L^2$-directions, between “models”. In the concrete context of the generalized parabolic Anderson model in 2D – one of the singular SPDEs discussed in the afore-mentioned article – we establish existence of a density at positive times.