Stochastic differential equations
A note on “Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions”
Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 99-104.

The eigenvalue problem of stochastic Hamiltonian systems with boundary conditions was studied by Peng [4] in 2000. For the one-dimensional case, denoting by {λ n } n=1 all the eigenvalues of such an eigenvalue problem, Peng proved that λ n + as n. In this short note, we prove that the growth order of λ n is the same as n 2 . Apart from the interest of this result in itself, the statistic periodicity of solutions of FBSDEs can be estimated directly by corresponding coefficients and time duration.

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DOI: 10.5802/crmath.103
Classification: 34L15, 60H10
Jing, Guangdong 1; Wang, Penghui 2

1 School of Mathematics, Shandong University Jinan, Shandong 250100, The People’s Republic of China
2 School of Mathematics, Shandong University Jinan, Shandong 250100, The People’s Republic of China.
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Jing, Guangdong; Wang, Penghui. A note on “Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions”. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 99-104. doi : 10.5802/crmath.103. http://www.numdam.org/articles/10.5802/crmath.103/

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[6] Wang, Haiyang; Wu, Zhen Eigenvalues of stochastic Hamiltonian systems driven by Poisson process with boundary conditions, Bound. Value Probl., Volume 2017 (2017), 164 | MR | Zbl

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