Moments of the number of upcrossings of an absolutely continuous process at points of density of a sample path derivative associated set

Douglas R. Anderson and Daniel D. Carpenter

Stochastic Processes and their Applications, 1982, vol. 13, issue 1, 27-37

Abstract: For a separable process on the unit interval with a.s. absolutely continuous sample paths a kth factorial moment formula is found for the number of sample path upcrossings of zero which occur at points of density (in a weak sense) of the set where the sample path derivative exceeds a fixed value. In the case where the sample path derivative is continuous on the closed unit interval the moment formula reduces to a simple variation of the Cramér-Leadbetter formula for the corresponding kth factorial moment of the number of unconstrained upcrossings.

Keywords: Zero; crossings; constrained; zero; crossings; absolutely; continuous; sample; paths; factorial; moments; point; processes; points; of; density (search for similar items in EconPapers)
Date: 1982
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(82)90004-7
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:spapps:v:13:y:1982:i:1:p:27-37

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

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().