\def\cprime{$'$} \def\cprime{$'$} \def\cprime{$'$} \def\cprime{$'$}
\begin{thebibliography}{10}

\bibitem{BandiniRusso1}
E.~Bandini and F.~Russo.
\newblock Weak {D}irichlet processes with jumps.
\newblock {\em {Stochastic Process. Appl.}}, 127(12):4139--4189, 2017.

\bibitem{BandiniRusso2}
E.~Bandini and F.~Russo.
\newblock Special weak {D}irichlet processes and {BSDE}s driven by a random
  measure.
\newblock {\em Bernoulli}, 24(4A):2569--2609, 2018.

\bibitem{BandiniRusso_DistrDrift}
E.~Bandini and F.~Russo.
\newblock Path-dependent {SDE}s with jumps and irregular drift: well-posedness
  and {D}irichlet properties.
\newblock {\em Preprint arXiv:2211.03444}, 2022.

\bibitem{BandiniRusso_RevisedWeakDir}
E.~Bandini and F.~Russo.
\newblock Weak {D}irichlet processes and generalized martingale problems.
\newblock {\em Preprint ar{X}iv:2205.03099}, 2022.

\bibitem{BLT}
B.~Bouchard, G.~Loeper, and X.~Tan.
\newblock A {{\(\mathbb{C}^{0, 1}\)}}-functional {It{\^o}}'s formula and its
  applications in mathematical finance.
\newblock {\em Stochastic Process. Appl.}, 148:299--323, 2022.

\bibitem{cjms}
F.~Coquet, A.~Jakubowski, J.~M{\'e}min, and L.~S{\l}omi{\'n}ski.
\newblock Natural decomposition of processes and weak {D}irichlet processes.
\newblock In {\em In memoriam {P}aul-{A}ndr\'e {M}eyer: {S}\'eminaire de
  {P}robabilit\'es {XXXIX}}, volume 1874 of {\em Lecture Notes in Math.}, pages
  81--116. Springer, Berlin, 2006.

\bibitem{nunno-book}
B.~Di~Nunno, G.~{\O}ksendal and F.~Proske.
\newblock {\em Malliavin calculus for {L}\'evy processes with applications to
  finance}.
\newblock Universitext. Springer-Verlag, Berlin, 2009.

\bibitem{er2}
M.~Errami and F.~Russo.
\newblock {$n$}-covariation, generalized {D}irichlet processes and calculus
  with respect to finite cubic variation processes.
\newblock {\em Stochastic Process. Appl.}, 104(2):259--299, 2003.

\bibitem{gr1}
F.~Gozzi and F.~Russo.
\newblock Verification theorems for stochastic optimal control problems via a
  time dependent {F}ukushima-{D}irichlet decomposition.
\newblock {\em Stochastic Process. Appl.}, 116(11):1530--1562, 2006.

\bibitem{gr}
F.~Gozzi and F.~Russo.
\newblock Weak {D}irichlet processes with a stochastic control perspective.
\newblock {\em Stochastic Process. Appl.}, 116(11):1563--1583, 2006.

\bibitem{chineseBook}
S.~He, J.~Wang, and J.~Yan.
\newblock {\em Semimartingale theory and stochastic calculus}.
\newblock Science Press Beijing New York, 1992.

\bibitem{JacodBook}
J.~Jacod.
\newblock {\em Calcul {S}tochastique et {P}robl\`emes de martingales}, volume
  714 of {\em Lecture Notes in Mathematics}.
\newblock Springer, Berlin, 1979.

\bibitem{jacod_book}
J.~Jacod and A.~N. Shiryaev.
\newblock {\em Limit theorems for stochastic processes}, volume 288 of {\em
  Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of
  Mathematical Sciences]}.
\newblock Springer-Verlag, Berlin, second edition, 2003.

\bibitem{rv95}
F.~Russo and P.~Vallois.
\newblock The generalized covariation process and {I}t\^o formula.
\newblock {\em Stochastic Process. Appl.}, 59(1):81--104, 1995.

\bibitem{Russo_Vallois_Book}
F.~Russo and P.~Vallois.
\newblock {\em Stochastic Calculus via Regularizations}, volume~11.
\newblock Springer International Publishing. Springer-Bocconi, 2022.

\bibitem{Stroock_Varadhan}
D.~W. Stroock and S.~S. Varadhan.
\newblock {\em Multidimensional diffusion processes}.
\newblock Springer, 2007.

\end{thebibliography}
