Papers Published
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.