HardStochastic Processes

Random Walk — Expected Steps

Jane StreetTwo Sigma

A symmetric random walk starts at 3 and stops when it hits 0 or 10 (each step ±1, equally likely). What is the expected number of steps until it stops?

Hints

Expected absorption time satisfies Ek=1+12Ek1+12Ek+1E_k = 1 + \tfrac12 E_{k-1} + \tfrac12 E_{k+1}.

The solution is k(Nk)k(N-k).

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