hal-01241073
https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073
https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073v2/document
https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073v2/file/E_FR_corrente1.pdf
arxiv:1512.06236
Weak Dirichlet processes with jumps
Bandini, Elena
Russo, Francesco
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
UNDEFINED
Weak Dirichlet processes
Calculus via regularizations
Random measure
Stochastic integrals for jump processes
Orthogonality
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 ] × R → 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 Itô type rule.
2016-12-16
2016-12-16
en