Weak Dirichlet processes with jumps.
2017
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastic Processes and their applications, vol. 12, pp. 4139--4189
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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-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}, }