On the asymptotic behaviour of a simple growing point process model
We consider a finite simple point process in space Rd evolving in discrete time in the following way. Starting with an arbitrary initial configuration, at each time step a point is chosen at random from the process according to a certain distribution, and then k new points are added to the process at locations, each obtained by adding an independent random vector to the location of the chosen "mother" point. The k "displacement vectors" are independent of each other and of the past evolution of the process, and follow a given common distribution that can depend on the time step (while the value of k remains fixed over time). Under mild moment conditions (uniform integrability and the existence of Cesaro limits for the sequences of respective moments for the displacement vectors), we obtain the limiting behaviour of the distribution of the point last added to the process and also that of the normalized mean measure of the point process as time goes to infinity.
Volume (Year): 72 (2005)
Issue (Month): 3 (May)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Asmussen, Soren & Kaplan, Norman, 1976. "Branching random walks I," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 1-13, January.
- Kaplan, Norman & Asmussen, Soren, 1976. "Branching random walks II," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 15-31, January.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:72:y:2005:i:3:p:265-275. 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: (Dana Niculescu)
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.