I can find the $i th$ term of a recurrence relationship $Y$ like this:
$\begin{equation} Y_i=\sigma_i+\beta_iY_{i-1} \end{equation}$ where $\sigma$ and $\beta$ are normally distributed random variables. I'd like to convert this into summation over $i=1..n$ something like this:
$\begin{equation} Y=\sigma_i+\displaystyle \sum_{i=2}^{n-1}\beta_iY_{i-1} \end{equation}$
I know this summation is wrong, any ideas?