A NOTE ON THE UPPER BOUND FOR IID LARGE DEVIATIONS
成果类型：
Article
署名作者：
DINWOODIE, IH
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990231
发表日期：
1991
页码：
1732-1736
关键词：
摘要：
Let X(n)BAR denote the mean of an i.i.d. sequence of random vectors X1, X2, X3,... taking values in R(d). If lambda denotes the convex conjugate of the logarithm of the moment generating function for X1, then lim sup 1/n log P(X(n)BAR is-an-element-of C) less-than-or-equal-to -inf{lambda(upsilon): upsilon is-an-element-of C} when C subset-of R(d) is closed and the moment generating function for X1 is finite in a neighborhood of the origin. An example is given in which this upper bound fails for a certain closed set in R3 and the moment generating function for X1 is not finite in a neighborhood of the origin. An example is also given in which this upper bound is valid for all closed sets but the moment generating function for X1 is not finite in a neighborhood of the origin.