Weak convergence with random indices


Journal Article

Suppose {Xnn≥-0} are random variables such that for normalizing constants an>0, bn, n≥0 we have Yn(·)=(X[n, ·]-bn/an ⇒ Y(·) in D(0.∞) . Then an and bn must in specific ways and the process Y possesses a scaling property. If {Nn} are positive integer valued random variables we discuss when YNn → Y and Y'n=(X[Nn]-bn)/an ⇒ Y'. Results given subsume random index limit theorems for convergence to Brownian motion, stable processes and extremal processes. © 1977.

Full Text

Duke Authors

Cited Authors

  • Durrett, RT; Resnick, SI

Published Date

  • January 1, 1977

Published In

Volume / Issue

  • 5 / 3

Start / End Page

  • 213 - 220

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/0304-4149(77)90031-X

Citation Source

  • Scopus