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- W4297197862 abstract "We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the sensitivities of processes, namely derivatives of martingale components and a weak notion of infinitesimal generators, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating martingales. The theory comes with convergence results that allow to interpret a large class of Wiener functionals beyond semimartingales as limiting objects of differential forms which can be computed path wisely over finite-dimensional spaces. The theory reveals that solutions of BSDEs are minimizers of energy functionals w.r.t Brownian motion driving noise." @default.
- W4297197862 created "2022-09-27" @default.
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- W4297197862 date "2017-07-16" @default.
- W4297197862 modified "2023-09-28" @default.
- W4297197862 title "A weak version of path-dependent functional It^o calculus" @default.
- W4297197862 doi "https://doi.org/10.48550/arxiv.1707.04972" @default.
- W4297197862 hasPublicationYear "2017" @default.
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