Consider a one-dimensional random walk on the integer lattice, starting at 0. The next step is decided to be +1 or -1 with equal probability 0.5. The hitting time (the expected time required for the random walk to reach any integer α -- also called the first-passage time) will be [itex]\Theta(\alpha^2)[/itex], since random walks are martingales. Similarly, given two numbers (α<0 and β>0), the expected time for the random walk to reach either α or β is α*β.(adsbygoogle = window.adsbygoogle || []).push({});

In my case, I have two or more independent random walks r_{1}, r_{2}, …, that run in parallel, and I want to find the expected time required for at least one of these random walks r_{i}to reach either α_{i}or β_{i}(notice that the boundaries α_{i}and β_{i}can be different for each random walk). My initial intuition was that, since these random walks are independent, I could find the hitting time for each random walk and get the minimum, but I found this to be wrong through a computer simulation.

Any pointers?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hitting time of two or three parallel random walks

Loading...

Similar Threads for Hitting three parallel |
---|

B Probability of loto hitting a specific place |

**Physics Forums | Science Articles, Homework Help, Discussion**