Orlicz Norms of Sequences of Random Variables
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چکیده
Let fi, i = 1, . . . , n, be copies of a random variable f and N be an Orlicz function. We show that for every x ∈ R the expectation E‖(xifi)i=1‖N is maximal (up to an absolute constant) if fi, i = 1, . . . , n, are independent. In that case we show that the expectation E‖(xifi)i=1‖N is equivalent to ‖x‖M , for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.
منابع مشابه
Orlicz Norms of Sequences of Random Variables by Yehoram Gordon,1 Alexander Litvak,2 Carsten Schütt3 And
Let fi , i = 1, . . . , n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ Rn the expectation E‖(xifi )i=1‖N is maximal (up to an absolute constant) if fi , i = 1, . . . , n, are independent. In that case we show that the expectation E‖(xifi)i=1‖N is equivalent to ‖x‖M , for some Orlicz function M depending on N and on distribution of f only. We prov...
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تاریخ انتشار 2007