  This work concerns about forward-backward multivalued stochastic systems.
First of all, we prove one average principle for general stochastic
differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a
convergence rate is presented. Then combining general stochastic differential
equations with backward stochastic variation inequalities, we establish the
other average principle for backward stochastic variation inequalities in the
$L^{2}$ sense through a time discretization method. Finally, we apply our
result to nonlinear parabolic partial differential equations and obtain the
homogenization of them.
