Uniform large and moderate deviations for functionalempirical processes
نویسنده
چکیده
For fX i g i1 a sequence of i.i.d. random variables taking values in a Polish space with distribution , we obtain large and moderate deviation principles for the processes fn ?1 P nt] i=1 X i ; t 0g n1 and fn ?1=2 P nt] i=1 (X i ?); t 0g n1 , respectively. Given a class of bounded functions F on , we then consider the above processes as taking values in the Banach space of bounded functionals over F and obtain the corresponding (uniform over F), large and moderate deviation principles. Among the corollaries considered are functional laws of the iterated logarithm.
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