uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Fixed points of inhomogeneous smoothing transforms
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2012 (English)In: Journal of difference equations and applications (Print), ISSN 1023-6198, E-ISSN 1563-5120, Vol. 18, no 8, 1287-1304 p.Article in journal (Refereed) Published
Abstract [en]

We consider the inhomogeneous version of the fixed-point equation of the smoothing transformation, that is, the equation X=C-d + Sigma(i >= 1) TiXi, where =(d) means equality in distribution, (C, T-1, T-2, . . .) is a given sequence of non-negative random variables and X-1, X-2, . . . is a sequence of i.i.d. copies of the non-negative random variable X independent of (C, T-1, T-2, . . .). In this situation, X (or, more precisely, the distribution of X) is said to be a fixed point of the (inhomogeneous) smoothing transform. In the present paper, we give a necessary and sufficient condition for the existence of a fixed point. Furthermore, we establish an explicit one-to-one correspondence with the solutions to the corresponding homogeneous equation with C = 0. Using this correspondence and the known theory on the homogeneous equation, we present a full characterization of the set of fixed points under mild assumptions.

Place, publisher, year, edition, pages
2012. Vol. 18, no 8, 1287-1304 p.
Keyword [en]
branching random walk, fixed point, multiplicative martingales, smoothing transform, stochastic fixed-point equation, weighted branching process
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-180298DOI: 10.1080/10236198.2011.589514ISI: 000306746300003OAI: oai:DiVA.org:uu-180298DiVA: diva2:549076
Available from: 2012-09-03 Created: 2012-09-03 Last updated: 2017-12-07Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text
By organisation
Mathematical Statistics
In the same journal
Journal of difference equations and applications (Print)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 411 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf