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Write the command for this recursive formula?

Posted 2 years ago
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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.

Posted 2 years ago

Hey guys,

I think I have solved my problem now. See my commands below.

However, welcome to any advice, efficiency or another programming method.

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