z****e
发帖数: 702 | 1 Xn为标准正态分布N(0,1),Sn为前n项和，求n
常数)
即求P[sup (Sn-an-b)>=0] <= ?
n
这个问题我利用e^(Sn-1/2)为鞅，和最大值不等式P(sup Mn >l)<=E(Mn)/l，
得到P<=e^-(a-1/2)n-b, 因为取n-->inf极限后，需要考虑a，b的取值。
所以总觉得我做错了。不知道我错在哪里了？本来是个挺简单的随机漫步的问题。 | o*******w
发帖数: 349 | 2 Yn = (X1 + X2 + ... + Xn)/n is of normal distribution with known mean, 0,
and variance, var(Xi)/n
Then to find Pr(Yn > a + b/n) is easy. | o*******w
发帖数: 349 | 3 Sorry, did not notice that Xi is not necessarily independent. | o*******w
发帖数: 349 | 4 This is a problem of "renewal processes". You can find results of them in
many text book. Basically, Sn is a normal distribution. |
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