Orlicz norms of sequences of random variables
نویسندگان
چکیده
منابع مشابه
Orlicz Norms of Sequences of Random Variables
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 appl...
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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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Chatterji [2] has formulated the following heuristic principle: given any limit property for independent identically distributed random variables (i.i.d.r.v.'s), there exists an analogous property such that an arbitrary sequence of r.v.'s always has some subsequence possessing this analogous property. By 'arbitrary', we mean that no assumption concerning dependence is made, though it may be nec...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2002
ISSN: 0091-1798
DOI: 10.1214/aop/1039548373