Return time moment of time-homogeneous and null-recurrent one-dimension diffusion with reflection boundary

This work aims to study moment of return time of time-homogeneous and null-recurrent one-dimension diffusion on 0,\infty ) with reflection boundary, to solve estimation of approximate solution of differential equation with reflection boundary satisfied by the Laplace transform in return time． Asymptotic estimation of probability distribution in return time is obtained using Tauberian lemma． When \gamma -moment is finite the range of order \gamma is calculated．