We show necessary and sufficient conditions for $R$-recurrence and \mbox{$R$-positivity} of one-dimensional diffusions killed at the origin. These conditions are stated in terms of the bottom eigenvalue function.
@article{1078415844,
author = {Mart\'\i nez, Servet and San Mart\'\i n, Jaime},
title = {Classification of killed one-dimensional diffusions},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 530-552},
language = {en},
url = {http://dml.mathdoc.fr/item/1078415844}
}
Martínez, Servet; San Martín, Jaime. Classification of killed one-dimensional diffusions. Ann. Probab., Tome 32 (2004) no. 1A, pp. 530-552. http://gdmltest.u-ga.fr/item/1078415844/