On non-continuous Dirichlet processes (Q1868452)

A Dirichlet process is an adapted càdlàg process that can be represented as the sum of a semimartingale and an adapted continuous process with zero quadratic variation. For continuous Dirichlet processes, a pathwise Itô calculus was introduced by \textit{H. Föllmer} [in: Séminaire de probabilités XV. Lect. Notes Math. 850, 143-150 (1981; Zbl 0461.60074) and in: Stochastic integrals. Lect. Notes Math. 851, 476-478 (1981; Zbl 0462.60046)]. In the paper under review, such results are obtained for non-continuous Dirichlet processes. In particular, it is shown that the class of Dirichlet processes is stable under \(C^1\) transforms.