@inbook{ca7cd8b91049490b8e439d9ca45087fd,
title = "Calculus via Regularization and Rough Paths",
abstract = "This chapter examines some relations between the stochastic calculus via regularizations and the celebrated deterministic rough path theory. We introduce the notion of a stochastically controlled process extending the one of controlled process introduced by M. Gubinelli. We show a precise relation between weak Dirichlet processes and stochastically controlled process. We also introduce a notion of stochastic rough integral, and we connect it with the symmetric integral via regularizations.",
author = "Francesco Russo and Pierre Vallois",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/978-3-031-09446-0\_17",
language = "English",
series = "Bocconi and Springer Series",
publisher = "Springer-Verlag Italia s.r.l.",
pages = "597--615",
booktitle = "Bocconi and Springer Series",
}