  This paper is concerned with high moment and pathwise error estimates for
both velocity and pressure approximations of the Euler-Maruyama scheme for time
discretization and its two fully discrete mixed finite element discretizations.
The main idea for deriving the high moment error estimates for the velocity
approximation is to use a bootstrap technique starting from the second moment
error estimate. The pathwise error estimate, which is sub-optimal in the energy
norm, is obtained by using Kolmogorov's theorem based on the high moment error
estimates. Unlike for the velocity error estimate, the higher moment and
pathwise error estimates for the pressure approximation are derived in a
time-averaged norm. In addition, the impact of noise types on the rates of
convergence for both velocity and pressure approximations is also addressed.
