Exact finite-N survival and last-return probabilities are derived for biased 1D random walks, including a critical bias above which the probability of last return decreases monotonically.
and Sokolov, I.M., First Steps in Random Walks: From Tools to Applications (Oxford University Press Inc., New York) 2011
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Exact closed-form recurrence probabilities for biased random walks at any step number
Exact finite-N survival and last-return probabilities are derived for biased 1D random walks, including a critical bias above which the probability of last return decreases monotonically.