Weak convergence with random indices |
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| Authors: | Richard T Durrett Sidney I Resnick |
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| Institution: | Stanford University, Stanford, California 94305, U.S.A. |
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| Abstract: | Suppose {Xnn?-0} are random variables such that for normalizing constants an>0, bn, n?0 we have Yn(·)=(Xn, ·]-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=(XNn]-bn)/an ? Y'. Results given subsume random index limit theorems for convergence to Brownian motion, stable processes and extremal processes. |
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| Keywords: | weak convergence random indices stable process Brownian motion extremal process regular variation mixing |
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