  New theorems for the moments of the first passage time of one dimensional
nonlinear stochastic processes with an entrance boundary are formulated. This
important class of one dimensional stochastic processes results among others
from approximations of the energy or amplitude of second order nonlinear
stochastic differential equations. Since the diffusion of a stochastic process
vanishes at an entrance boundary, the entrance boundary is called a singular
point of the stochastic process. The theorems for the moments of the first
passage times are validated based on existing analytical results. In addition,
the first passage times of a nonlinear stochastic differential equation, which
is important for the determination of dangerous ship roll dynamics, are
calculated. The proposed analytical expressions for the moments of the first
passage times can be calculated very fast using standard quadrature formulas.
