$\def\left{\operatorname{left}}\def\right{\operatorname{right}}$I have the following recurrence with cases: $$ p(l, r, s) = 0.5 \cdot \left(l, r, s) + 0.5 \cdot \right(l, r, s) $$ where: $$ \left(l, r, s) = \begin{cases} p(l - s, r, 2s) & s \le l\\ 1 & l < s \le l + w\\ 0 & l + w < s\end{cases} $$
$$ \right(l, r, s) = \begin{cases} p(l, r - s, 2 s) & s \le r\\ 1 & r < s \le r + w\\ 0 & r + w < s\end{cases}$$
Is there a way to solve this recurrence analytically?
I'm interested in finding a solution for parameters such that $l = r = k$, $s = 1$ and $w = f\cdot k$, where $f \in (0, 1)$.
If not, is there a way to solve this analytically for a fixed $k$?
wis some fraction ofk, that iswis in the interval(0, 1). Thanks for fixing it. – axel22 Dec 10 '12 at 14:17$...$for mathematical text. – martini Dec 10 '12 at 14:20