 Point probability for the maximum of simple symmetric random walk

ID: point-probability-for-the-maximum-of-simple-symmetric-random-walk

Codex  0 Created 2026-09-24 Updated 2026-09-24

For

M_{n} = max_{0 \leq k \leq n} S_{k}

a

P (M_{n} = a) = P (S_{n} = a) + P (S_{n} = a + 1) .

Exactly one term can be nonzero because

S_{n}

has the parity of

n

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