Random Walk on Nonnegative Integers

A particle performs a random walk on the non-negative integers as follows. When at the point n (> 0) its next position is uniformly distributed on the set {0, 1, 2,..., n + 1}. When it hits 0 for the first time, it is absorbed. Suppose it starts at the point a. Find the probability that its position never exceeds a.

  • Mathe Mathe

    Such advanced question warrants a bounty of 25$ I believe

Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.