Some remarks on local time-space calculus

Xiangfeng Yang and Litan Yan

Statistics & Probability Letters, 2007, vol. 77, issue 16, 1600-1607

Abstract: Let X be a reversible semi-martingale satisfying certain conditions and let be a locally bounded measurable function such that it admits locally bounded Radon-Nikodym derivatives [not partial differential]F/[not partial differential]t and [not partial differential]F/[not partial differential]x, then the following change-of-variable formula is valid: where is the local time of X at x, and denotes the stochastic area integral with respect to defined by Eisenbaum [2006. Local time-space stochastic calculus for Lévy processes. Stochastic process and Appl. 116, 757-778]. Furthermore, some results are extended from deterministic integrated functions to random functions. We establish the conditions for the existence of such stochastic area integration and give some representations of this integral.

Keywords: Local; time; Reversible; semi-martingale; Local; time-space; calculus (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00135-6
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:77:y:2007:i:16:p:1600-1607

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().