  The approximative theorems of incomplete Riemann-Stieltjes sums of Ito
stochastic integral, mean square integral and Stratonovich stochastic integral
with respect to Brownian motion are investigated. Some sufficient conditions of
incomplete Riemann-Stieltjes sums approaching stochastic integral are
developed, which establish the alternative ways to converge stochastic
integral. And, Two simulation examples of incomplete Riemann-Stieltjes sums
about Ito stochastic integral and Stratonovich stochastic integral are given
for demonstration.
