Hey guys:
I have following recursive formula:
\mathbb{E}[Z_t^n]=\sum_{k=0}^{n-1}\binom{n}{k}\mathbb{E}[X^{n-k} ][\int_0^t e^{-n \delta v} \mathbb{E}[Z_{t-v}^k] dm(v)]
where \mathbb{E} is the expectation of random variable. You may assume X is exponential distributed and m(t)=\lambda t, \lambda>0. Further, \mathbb{E}[Z_t^0]=1.
I am wondering how can I write the commands to achieve \mathbb{E}[Z_t^n] for n large, no matter numerically or theoretically.
Thanks in advance.