Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalues of stochastic Hamiltonian systems with boundary conditions
  and its application   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.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn