Weak Dirichlet processes with jumps.
2017
Type de publication :
Article (revues avec comité de lecture)
Journal :
Stochastic Processes and their applications, vol. 12, pp. 4139--4189
HAL :
arXiv :
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 :
@article{Ban-Rus-2017,
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 },
pages={4139--4189},
}