Weak Dirichlet processes with jumps

被引：9

作者：

Bandini, Elena ^{[1
]}

Russo, Francesco ^{[2
]}

机构：

[1] LUISS Roma, Dipartimento Econ & Finanza, Via Romania 32, I-00197 Rome, Italy

[2] Univ Paris Saclay, ENSTA ParisTech, Unite Math Appl, 828 Blvd Marechaux, F-91120 Palaiseau, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2017年 / 127卷 / 12期

关键词：

Weak Dirichlet processes; Calculus via regularizations; Random measure; Stochastic integrals for jump processes; Orthogonality; ITO FORMULA; GENERALIZED COVARIATION; CALCULUS; SEMIMARTINGALES; DECOMPOSITION; INTEGRATION; BACKWARD;

D O I：

10.1016/j.spa.2017.04.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued cadlag 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] x R -> R, which is of class C-0,C-1 (or sometimes less), we provide a chain rule type expansion for u(t, X-t) which stands in applications for a chain Ito type rule. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：4139 / 4189

页数：51

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