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• W2738919127 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.
• W2738919127 created "2017-07-31" @default.
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• W2738919127 date "2017-07-17" @default.
• W2738919127 modified "2023-09-27" @default.
• W2738919127 title "A weak version of path-dependent functional It^o calculus" @default.
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