@inbook{934a0dc094e44d8c8f65b32dcbedaf6f,
title = "Stability of the Covariation and It{\^o}{\textquoteright}s Formula",
abstract = "We show, in an abstract framework, that the quadratic variation is stable by C1 functions, and we express It{\^o} formulae for C2 functions of finite quadratic variation processes. We apply those formulae to semimartingales, and we illustrate a first approach to stochastic differential equations (driven by a forward or It{\^o} integral). We also introduce the L{\'e}vy area between two processes by regularizations methods.",
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\_6",
language = "English",
series = "Bocconi and Springer Series",
publisher = "Springer-Verlag Italia s.r.l.",
pages = "199--232",
booktitle = "Bocconi and Springer Series",
}