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Consider the random walk $S_n$ given by: $$ S_{n+1}= \left\{ \begin{array}{ll} S_n + 2 & \mbox{w.p } p\\ S_n -1 & \mbox{w.p } 1-p \end{array} \right. $$ Assume that $S_0=n > 0$ with certainty. What is the probability of eventually reaching the origin (the point 0) ?

Now I know the derivation for the same problem but when it's symmetric and unbiased namely the additions are $1,-1$ with probability $\frac{1}{2}$ for each. Can I use this result or that I need to make the derivation from the start?

Hanna Khalil
  • 388
  • not clear you can reuse the same result. This walk is biased, so larger p means you will have drift; also skipping one may be a problem -- i.e. you can reach -1, and then skip over to 1 if $n<0$. – gt6989b Apr 29 '15 at 18:02
  • I will edit now but $n > 0$ – Hanna Khalil Apr 29 '15 at 18:07

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