I've got a problem involving a recurrent expression. I would like to find a solution of $x_t$ that let me take derivatives or finding the minimum of the function. Does anybody know tools for solving this problem?
$x_t = [k_1 + (1-k_1)·x_{t-1}] · [1-k_2·(1-[1-k_1]^{t-1})]$
Where $k_1$ and $k_2$ are constants. Note that the second terms includes the $t$ variable. Also to point out is that:
$x_0 = 0$
If anyone could solve it, it would be great, but what i'm asking for is if anyone knows tools for solving this kind of functions, i'm kind of lost.
Thanks in advance!
I don't know how to solve it.
If you ask me what tools can be used, however, Mathematica is the best for this kind of symbolic problems.
For the result of Mathematica, it gives
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