On the Markov property of some Brownian martingales
Let hn be the (probabilists’) Hermite polynomial of degree n. Let Hn(z,a)=an/2hn(z/a) and Hn(z,0)=zn. It is well-known that Hn(Bt,t) is a martingale for every n. In this paper, we show that for n≥3, Hn(Bt,t) is not Markovian. We then give a brief discussion on mimicking Hn(Bt,t) in the sense of constructing martingales whose marginal distributions match those of Hn(Bt,t).
If you experience problems downloading a file, check if you have the
view it first. In case of further problems read
the IDEAS help
. Note that these files are not
on the IDEAS
site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Article provided by Elsevier in its journal Stochastic Processes and their Applications
Volume (Year): 122 (2012)Handle:
Issue (Month): 10 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Related researchKeywords: Brownian martingales
; Hermite polynomials
; Markov property
; Mimicking selfsimilar martingales
ReferencesNo references listed on IDEAS
You can help add them by filling out this form
This item is not listed on Wikipedia, on a reading list
or among the top items
StatisticsAccess and download statistics
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:122:y:2012:i:10:p:3506-3512. See general information
about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.