Infinite-dimensional calculus under weak spatial regularity of the processes

F. Flandoli, F. Russo, G.A. Zanco, Journal of Theoretical Probability 31 (2018) 789–826.

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Journal Article | Published | English
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Abstract
Two generalizations of Itô formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations when they occur in examples and it is applied to the case of a group generator. The second one, based on the previous one and a limit procedure, is an Itô formula in a special class of Banach spaces having a product structure with the noise in a Hilbert component; again the key point is the extension due to a cancellation. This extension to Banach spaces and in particular the specific cancellation are motivated by path-dependent Itô calculus.
Publishing Year
Date Published
2018-06-01
Journal Title
Journal of Theoretical Probability
Acknowledgement
Open access funding provided by Institute of Science and Technology (IST Austria). The second named author benefited partially from the support of the “FMJH Program Gaspard Monge in Optimization and Operations Research” (Project 2014-1607H). He is also grateful for the invitation to the Department of Mathematics of the University of Pisa. The third named author is grateful for the invitation to ENSTA.
Volume
31
Issue
2
Page
789-826
IST-REx-ID

Cite this

Flandoli F, Russo F, Zanco GA. Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. 2018;31(2):789-826. doi:10.1007/s10959-016-0724-2
Flandoli, F., Russo, F., & Zanco, G. A. (2018). Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability, 31(2), 789–826. https://doi.org/10.1007/s10959-016-0724-2
Flandoli, Franco, Francesco Russo, and Giovanni A Zanco. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” Journal of Theoretical Probability 31, no. 2 (2018): 789–826. https://doi.org/10.1007/s10959-016-0724-2.
F. Flandoli, F. Russo, and G. A. Zanco, “Infinite-dimensional calculus under weak spatial regularity of the processes,” Journal of Theoretical Probability, vol. 31, no. 2, pp. 789–826, 2018.
Flandoli F, Russo F, Zanco GA. 2018. Infinite-dimensional calculus under weak spatial regularity of the processes. Journal of Theoretical Probability. 31(2), 789–826.
Flandoli, Franco, et al. “Infinite-Dimensional Calculus under Weak Spatial Regularity of the Processes.” Journal of Theoretical Probability, vol. 31, no. 2, Springer, 2018, pp. 789–826, doi:10.1007/s10959-016-0724-2.
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