This paper develops systematically the 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. Given a function u:[0,T]×R→R, 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 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. Given a function u:[0,T]×R→R, 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
Articolo in rivista - Articolo scientifico
Calculus via regularizations; Orthogonality; Random measure; Stochastic integrals for jump processes; Weak Dirichlet processes; Statistics and Probability; Modeling and Simulation; Applied Mathematics
English
2017
127
12
4139
4189
reserved
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/179696
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