Abstract
In this paper we study two notions of differentiability introduced by P. Cannarsa and G. Da Prato (see [28]) and L. Gross (see [56]) in both the framework of infinite dimensional analysis and the framework of Malliavin calculus.
Funding Statement
The authors are members of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of the Italian Istituto Nazionale di Alta Matematica (INdAM). Davide A. Bignamini and Simone Ferrari have been partially supported by the INdAM-GNAMPA Project 2023 “Equazioni differenziali stocastiche e operatori di Kolmogorov in dimensione infinita” CUP_E53C22001930001. Margherita Zanella has been partially supported by the INdAM-GNAMPA Project 2023 “Analisi qualitativa di PDE e PDE stocastiche per modelli fisici” CUP_E53C22001930001. The authors have no relevant financial or non-financial interests to disclose.
Acknowledgments
The authors are grateful to E. Priola and L. Tubaro for numerous useful comments and discussions.
Citation
Davide A. Bignamini. Simone Ferrari. Simona Fornaro. Margherita Zanella. "Differentiability in infinite dimension and the Malliavin calculus." Probab. Surveys 21 28 - 66, 2024. https://doi.org/10.1214/24-PS26
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