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Weak convergence with random indices

Author

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  • Durrett, Richard T.
  • Resnick, Sidney I.

Abstract

Suppose {Xnn[greater-or-equal, slanted]-0} are random variables such that for normalizing constants an>0, bn, n[greater-or-equal, slanted]0 we have Yn(·)=(X[n, ·]-bn/an => Y(·) in D(0.[infinity]) . 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.

Suggested Citation

  • Durrett, Richard T. & Resnick, Sidney I., 1977. "Weak convergence with random indices," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 213-220, July.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:3:p:213-220
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    Cited by:

    1. Wu, Biao, 2008. "On the weak convergence of subordinated systems," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3203-3211, December.

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