w*z
发帖数: 71 | 1 Without constraints on X(t), nobody can find the solution.
Suppose P(X(0)=0)=1, X(s1)-X(s0), ... , X(sn)-X(s n-1) are independent and
X(s_k)-X(s_{k-1}) has N(0, s_k- s_{k-1}), for any 0=s0<=s1<=...<=s_n=t, then
the pdf of \int_0^t X(s)ds can be found by taking the limit of the integral
sum.
If I am doing correctly, it should be N(0,t^3 /3).
In this case, X(t) and \int_0^t X(s)ds should be jointly normal.
And the correlation can be computed the same way. |
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