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 proper application to view it first. In case of further problems read the IDEAS help page. 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.
Volume (Year): 122 (2012)
Issue (Month): 10 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.