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.
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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}
}
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21 pages, 0 figures