A note on "Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions"

Abstract

The eigenvalue problem of stochastic Hamiltonian systems with boundary conditions was studied by Peng \cite{peng} in 2000. For one-dimensional case, denoting by $\{{\lambda }_n{\}}_{n=1}^{\infty }$ all the eigenvalues of such an eigenvalue problem, Peng proved that ${\lambda }_n\to +\infty$. In this short note, we prove that the growth order of ${\lambda }_n$ is the same as $n^2$ as $n\to +\infty$. Apart from the interesting of its own, by this result, the statistic period of solutions of FBSDEs can be estimated directly by corresponding coefficients and time duration.

arXiv comment7 pages

References in corpus (1)

• On well-posedness of forward-backward SDEs-A unified approach