Asymptotic survival probability of random walks on a semi-infinite line

Symmetric and asymmetric random walks on a segment (−∞,T>0) of the real line are considered. There is a non-zero probability for the random walk to get absorbed at a site it visits. We derive for such random walks, expressions for survival probabilities in the asymptotic limit ofT→∞. An application of this asymptotic formulation to the problem of radiation transport through thick shields is presented.