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Asymptotic expansions for random walks conditioned to stay positive

Denis Denisov et al.

Electronic Journal of Probability2026https://doi.org/10.1214/25-ejp1467article
ABDC A
Weight
0.37

Abstract

We consider a one-dimensional random walk Sn with i.i.d. increments with zero mean and finite variance. We derive asymptotic expansions for the tail distribution P(τx>n) of the first passage times τx:=inf{n≥1:x+Sn≤0}, x≥0. We also derive asymptotic expansion for local probabilities P(Sn=x,τ0>n). Studying the asymptotic expansions we obtain a sequence of discrete polyharmonic functions and obtain analogues of renewal theorem for them.

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https://doi.org/https://doi.org/10.1214/25-ejp1467

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@article{denis2026,
  title        = {{Asymptotic expansions for random walks conditioned to stay positive}},
  author       = {Denis Denisov et al.},
  journal      = {Electronic Journal of Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-ejp1467},
}

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Asymptotic expansions for random walks conditioned to stay positive

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Evidence weight

0.37

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.16 × 0.4 = 0.06
M · momentum0.53 × 0.15 = 0.08
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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