Rough paths and regularization

december, 2021
Publication type:
Paper in peer-reviewed journals
Journal of Stochastic Analysis (JOSA)., vol. 2 (4), pp. 1-21
assets/images/icons/icon_arxiv.png 2106.08054
Keywords :
Rough paths; calculus via regularizations; Gubinelli's derivative.
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.
    author={André O. Gomes and Alberto Ohashi and Francesco Russo and 
           Alan Teixeira },
    title={Rough paths and regularization },
    doi={10.31390/josa.2.4.01 },
    journal={Journal of Stochastic Analysis (JOSA). },
    year={2021 },
    volume={2 (4) },