Asymptotics of weighted random sums

• Verfasst von: Corcuera, José Manuel [VerfasserIn]
• Verfasst von: Nualart, David [VerfasserIn]
• Verfasst von: Podolskij, Mark [VerfasserIn]
• Titel: Asymptotics of weighted random sums
• Verf.angabe: José Manuel Corcuera, David Nualart, Mark Podolskij
• Fussnoten: Gesehen am 29.05.2018
• Titel Quelle: Enthalten in: Communications in applied and industrial mathematics
• Jahr Quelle: 2014
• Band/Heft Quelle: 6(2014,1) Artikelnummer e-486, 11 Seiten
• ISSN Quelle: 2038-0909
• DOI: doi:10.1685/journal.caim.486
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1575820102

Abstract

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 observation distances 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: J. M. Corcuera, D. Nualart, and J. H. C. Woerner, Power variation of some integral fractional processes, Bernoulli, vol. 12, no. 4, pp. 713-735, 2006.