Aarhus University Seal / Aarhus Universitets segl

Asymptotics of weighted random sums

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Documents

  • pdf

    110 KB, PDF document

DOI

  • José Manuel Corcuera, University of Barcelona, Denmark
  • David Nualart, University of Kansas
  • ,
  • Mark Podolskij
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the weight process with respect to the Brownian motion when the distance between observations goes to zero. The result is obtained with the help of fractional calculus showing the power of this technique. This study, though interesting by itself, is motivated by an error found in the proof of Theorem 4 in Corcuera, J.M. Nualart, D., Woerner, J. H. C. (2006). Power variation of some integral fractional processes, Bernoulli 12(4) 713-735.
Original languageEnglish
Article numbere-486
JournalCommunications in Applied and Industrial Mathematics
Volume6
Issue1
ISSN2038-0909
DOIs
Publication statusPublished - 6 Feb 2014

    Research areas

  • math.PR, 60F17, 26A33

See relations at Aarhus University Citationformats

Download statistics

No data available

ID: 79219368