Weak Dirichlet processes with jumps.

Type de publication :
Article (revues avec comité de lecture)
Journal :
Stochastic Processes and their applications, vol. 12, pp. 4139--4189
arXiv :
assets/images/icons/icon_arxiv.png 1512.06236
Mots clés :
Weak Dirichlet processes; Calculus via regularizations; Random measure; Stochastic integrals for jump processes; Orthogonality.
Résumé :
This paper develops systematically stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued càdlàg weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process $A$ such that $[N,A] = 0$, for any continuous local martingale $N$. In particular, given a function $u:[0,T] \times \R \rightarrow \R$, which is of class $C^{0,1}$ (or sometimes less), we provide a chain rule type expansion for $X_t=u(t,X_t)$ which stands in applications for a chain It\^o type rule.
BibTeX :
    author={Elena Bandini and Francesco Russo },
    title={Weak Dirichlet processes with jumps. },
    doi={10.1016/j.spa.2017.04.001 },
    journal={Stochastic Processes and their applications },
    year={2017 },
    volume={12 },