Weak Dirichlet processes with jumps

Elena Bandini; Francesco Russo

doi:10.1016/j.spa.2017.04.001

Weak Dirichlet processes with jumps

Elena Bandini
, Francesco Russo

LUISS University
Université Paris-Saclay

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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 C^0,1 (or sometimes less), we provide a chain rule type expansion for u(t,X_t) which stands in applications for a chain Itô type rule.

Original language	English
Pages (from-to)	4139-4189
Number of pages	51
Journal	Stochastic Processes and their Applications
Volume	127
Issue number	12
DOIs	https://doi.org/10.1016/j.spa.2017.04.001
Publication status	Published - 1 Dec 2017
Externally published	Yes

Keywords

Calculus via regularizations
Orthogonality
Random measure
Stochastic integrals for jump processes
Weak Dirichlet processes

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10.1016/j.spa.2017.04.001

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title = "Weak Dirichlet processes with jumps",

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 c{\`a}dl{\`a}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]{\texttimes}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 It{\^o} type rule.",

keywords = "Calculus via regularizations, Orthogonality, Random measure, Stochastic integrals for jump processes, Weak Dirichlet processes",

author = "Elena Bandini and Francesco Russo",

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T1 - Weak Dirichlet processes with jumps

AU - Bandini, Elena

AU - Russo, Francesco

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Calculus via regularizations

KW - Orthogonality

KW - Random measure

KW - Stochastic integrals for jump processes

KW - Weak Dirichlet processes

U2 - 10.1016/j.spa.2017.04.001

DO - 10.1016/j.spa.2017.04.001

M3 - Article

AN - SCOPUS:85018390336

SN - 0304-4149

VL - 127

SP - 4139

EP - 4189

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 12

ER -

Weak Dirichlet processes with jumps

Abstract

Keywords

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