This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued cà dlà g 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. Given a function u:[0,T]ÃRâR, which is of class C0,1(or sometimes less), we provide a chain rule type expansion for u(t,Xt) which stands in applications for a chain Itô type rule
Bandini, E., Russo, F. (2017). Weak Dirichlet processes with jumps. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 127(12), 4139-4189 [10.1016/j.spa.2017.04.001].
Weak Dirichlet processes with jumps
Bandini, E;
2017
Abstract
This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued cà dlà g 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. Given a function u:[0,T]ÃRâR, which is of class C0,1(or sometimes less), we provide a chain rule type expansion for u(t,Xt) which stands in applications for a chain Itô type rule
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