It comes from the book Probability: Theory and Example. I don't understand the part marked with red line. Why it cannot converge to an interior point of $(a,b)$?
Can anyone help? Thanks so much!
2026-03-30 01:29:43.1774834183
Asymmetric simple random walk?
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Since the random walk has $+-1$ valued steps, converging to an interior point means that the walker has to remain at that point for every step after a certain time, which is impossible.