  In this paper we solve the eigenvalue problem of stochastic Hamiltonian
system with boundary conditions. Firstly, we extend the results in S. Peng
\cite{peng} from time-invariant case to time-dependent case, proving the
existence of a series of eigenvalues $\{\lambda_m\}$ and construct
corresponding eigenfunctions. Moreover, the order of growth for these
$\{\lambda_m\}$ are obtained: $\lambda_m\sim m^2$, as $m\rightarrow+\infty$. As
applications, we give an explicit estimation formula about the statistic period
of solutions of Forward-Backward SDEs. Besides, by a meticulous example we show
the subtle situation in time-dependent case that some eigenvalues appear when
the solution of the associated Riccati equation does not blow-up, which does
not happen in time-invariant case.
