Math @ Duke

Publications [#243429] of Richard T. Durrett
Papers Published
 Durrett, RT; Resnick, SI, Weak convergence with random indices,
Stochastic Processes and their Applications, vol. 5 no. 3
(1977),
pp. 213220, ISSN 03044149 [doi]
(last updated on 2017/12/15)
Abstract: 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.


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