邵宇     书的452页有这个题目的证明，即exp内是均值加上等式左边期望中分子的平方的1/2。具体的我公式打不上去
     
       

 虚数的平方为-1，把W(t)改为dW(t)=W(t)-W(0)的平方是t，因为W（0）是0没关系

[此贴子已经被作者于2008-2-1 11:04:36编辑过]

By the definition of Brownian Motion, for given t, W(t) is a normally distributed random variable with mean zero and variance t. All you need to do is just to calculate the characteristic function of this random variable. i.e. to calculate the expectation of
exp(i*ksi*W), where W has a distribution N(0,t), and "ksi" represents the Greek letter.

原来是矩母函数，明白了，谢谢两位！