%0 Unpublished work
%T Weak Dirichlet processes with jumps
%+ Politecnico di Milano [Milan] (POLIMI)
%+ Unité de Mathématiques Appliquées (UMA)
%A Bandini, Elena
%A Russo, Francesco
%Z The second named author benefitedpartially from the support of the ``FMJH Program Gaspard Monge in optimizationand operation research'' (Project 2014-1607H)
%8 2016-12-16
%D 2016
%Z 1512.06236
%K Weak Dirichlet processes
%K Calculus via regularizations
%K Random measure
%K Stochastic integrals for jump processes
%K Orthogonality
%Z 60J75; 60G57; 60H05
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073v2/document
%2 https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073v2/file/E_FR_corrente1.pdf
%L hal-01241073
%U https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073