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Journal Articles Journal of Stochastic Analysis Year : 2021

ROUGH PATHS AND REGULARIZATION

Abstract

Calculus via regularizations and rough paths are two methods to approach stochastic integration and calculus close to pathwise calculus. The origin of rough paths theory is purely deterministic, calculus via regularization is based on deterministic techniques but there is still a probability in the background. The goal of this paper is to establish a connection between stochastically controlled-type processes, a concept reminiscent from rough paths theory, and the so-called weak Dirichlet processes. As a by-product, we present the connection between rough and Stratonovich integrals for càdlàg weak Dirichlet processes integrands and continuous semimartingales integrators.
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Dates and versions

hal-03260855 , version 1 (15-06-2021)
hal-03260855 , version 2 (05-03-2024)

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André O Gomes, Alberto Ohashi, Francesco Russo, Alan Teixeira. ROUGH PATHS AND REGULARIZATION. Journal of Stochastic Analysis , 2021, 2 (4), pp.1-21. ⟨10.31390/josa.2.4.01⟩. ⟨hal-03260855v2⟩

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