Publications [#243429] of Richard T. Durrett

Papers Published

1. Durrett, RT; Resnick, SI, Weak convergence with random indices, Stochastic Processes and their Applications, vol. 5 no. 3 (January, 1977), pp. 213-220, Elsevier BV, ISSN 0304-4149 [doi]
   (last updated on 2024/08/31)

   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.