Weak Dirichlet processes with jumps.

to appear
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastic Processes and their applications
arXiv:
images/icons/icon_arxiv.png 1512.06236
Keywords :
Weak Dirichlet processes; Calculus via regularizations; Random measure; Stochastic integrals for jump processes; Orthogonality.
Abstract:
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:
@article{Ban-Rus-2100-1,
    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={to appear },
}