Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let's consider an asymmetric Random Walk on $Z$, with transition probabilities $p_{i, i+1}=p$, $~~p_{i, i+1}=q$, $\forall i \in \mathcal{Z}$, $p+q=1$ and $p>q$.

I am interested in the probability of the first hitting time of a bareer in $i=n$, assuming that the walk started from $i=0$ at time $t=0$. Is there an explicit formula for it? How does it depend on $n$?

share|improve this question
    
This is an exercise. The reflection principle lets you count the walks which first arrive at $n$ at time $t$. These all have the same probability, since they all have $n$ more positive steps than negative steps. –  Douglas Zare Mar 11 '13 at 17:28
    
This has been answered fully in math.stackexchange.com/questions/64919/… –  Jeremy Voltz Mar 11 '13 at 17:56
    
The answer by Did suggests another solution by generating functions but the reflection method is much simpler. –  Douglas Zare Mar 11 '13 at 20:14

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.