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Generating Functions for Asymmetric Random Walk Processes With Double Absorbing Barriers

Probability 2022-12-21 v1 Combinatorics

Abstract

Generating functions for asymmetric step-size paths restricted by two absorbing barriers are derived. The method begins by applying the Lagrange inversion formula to arbitrary powers of roots of the characteristic equation, that being a trinomial, which produces generating function as function (z) of the conditional probability of absorption of a particle, on a path restricted by two absorbing barriers. The exact enumeration of an asymmetric walk with two absorbing barriers is given.

Keywords

Cite

@article{arxiv.2212.09919,
  title  = {Generating Functions for Asymmetric Random Walk Processes With Double Absorbing Barriers},
  author = {Cetin Hakimoglu-Brown},
  journal= {arXiv preprint arXiv:2212.09919},
  year   = {2022}
}

Comments

21 pages, 0 figures

R2 v1 2026-06-28T07:43:33.128Z