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

2021/01/04 by Guangdong Jing, Jing, Guangdong, Penghui Wang +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #34L15 #60H10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2101.00894

openalex publication_date 2021/01/04 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

The eigenvalue problem of stochastic Hamiltonian systems with boundary conditions was studied by Peng \citepeng in 2000. For one-dimensional case, denoting by \λ_n\_n=1^∞ all the eigenvalues of such an eigenvalue problem, Peng proved that λ_n→ +∞. In this short note, we prove that the growth order of λ_n is the same as n² as n→ +∞. 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.

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