Hi I need help solving the following difference equation:
$ X_{t} b_{t-1} = X_{t-1} b_{t-2} - C_{t-1}$
where X and C are vectors and b is a scalar. Is there a way I can solve this for X?
2026-04-24 14:29:44.1777040984
Help solving vector difference equation
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Calling
$$ Y_t = X_t b_{t-1} $$
we have
$$ Y_t-Y_{t-1} = C_{t-1} $$
with solution
$$ Y_t = c_0 + \sum_{k=0}^{t-1}C_k = X_t b_{t-1} $$