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I'm stuck on a recurrence relation that arises in a simulation I'm writing. Does anybody know how to proceed on this? I'm not even sure, because of the variable coefficient, how to get the associated homogeneous case.

$ w_t = w_{t-1} \epsilon (1-u_t) + \epsilon u_t $

$\epsilon$ is a constant and ${u_t}$ is a binary sequence

Thanks

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    @Aryabhata: Although either a closed form or the "steady state" would be fine, I'd prefer a closed form.2012-03-20

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Whenever $u_t=1$, we have $w_t=\epsilon$, and whenever $u_t=0$, we have $w_t=w_{t-1}\epsilon$. Thus the sequence consists of initial segments of the geometric sequence $\epsilon^n$ and restarts at $\epsilon$ whenever $u_t=1$.

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    Thanks, I will do just that.2012-03-20