Regularity and decomposition of two-parameter supermartingales

G. Mazziotto and E. Merzbach

Journal of Multivariate Analysis, 1985, vol. 17, issue 1, 38-55

Abstract: The well-known Doob-Meyer decomposition of a supermartingale as the difference of a martingale and an increasing process is extended in several ways for two-parameter stochastic processes. In particular, the notion of laplacian is introduced which gives more explicit decomposition for potentials. The optional sampling theorem is stated for a wide class of supermartingales justifying the study of local martingales. Conditions for regularity and continuity for two-parameter processes are given using approximate laplacians. By introducing the notion of optional increasing path, the relation between the regularity of certain quasimartingales and the continuity of the associated integrable variation process is proved.

Keywords: Stopping; points; optional; increasing; paths; two-parameter; processes; supermartingales; potential; regularity (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(85)90093-4
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:jmvana:v:17:y:1985:i:1:p:38-55

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

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().