Stable Convergence and Stable Limit Theorems by Erich Häusler & Harald Luschgy

Author:Erich Häusler & Harald Luschgy
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

by definition requires independence of and so that the assumption of -measurability of makes no sense now for a nonconstant .

Example 6.12

Let be an independent sequence of standard normal random variables, and let be two continuous functions with and . For all and we set

and with . Then is an array of square integrable random variables adapted to , and this array is nested because for all and . Since the are independent standard normal random variables, for all and we obtain

and

whereas for all even and

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