The eigenvalue problem of stochastic Hamiltonian systems with boundary conditions was studied by Peng [4] in 2000. For the one-dimensional case, denoting by all the eigenvalues of such an eigenvalue problem, Peng proved that as . In this short note, we prove that the growth order of is the same as . 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.
Revised:
Accepted:
Published online:
Guangdong Jing 1; Penghui Wang 2
@article{CRMATH_2021__359_1_99_0, author = {Guangdong Jing and Penghui Wang}, title = {A note on {{\textquotedblleft}Problem} of eigenvalues of stochastic {Hamiltonian} systems with boundary conditions{\textquotedblright}}, journal = {Comptes Rendus. Math\'ematique}, pages = {99--104}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {1}, year = {2021}, doi = {10.5802/crmath.103}, language = {en}, }
TY - JOUR AU - Guangdong Jing AU - Penghui Wang TI - A note on “Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions” JO - Comptes Rendus. Mathématique PY - 2021 SP - 99 EP - 104 VL - 359 IS - 1 PB - Académie des sciences, Paris DO - 10.5802/crmath.103 LA - en ID - CRMATH_2021__359_1_99_0 ER -
Guangdong Jing; Penghui Wang. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.103/
[1] Solution of forward-backward stochastic differential equations, Probab. Theory Relat. Fields, Volume 103 (1995) no. 2, pp. 273-283 | MR | Zbl
[2] Solving forward-backward stochastic differential equations explicitly — a four step scheme, Probab. Theory Relat. Fields, Volume 98 (1994) no. 3, pp. 339-359 | MR | Zbl
[3] On well-posedness of forward-backward SDEs — a unified approach, Ann. Appl. Probab., Volume 25 (2015) no. 4, pp. 2168-2214 | MR | Zbl
[4] Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions, Stoch. Proc. Appl., Volume 88 (2000) no. 2, pp. 259-290 | DOI | MR | Zbl
[5] Fully coupled forward-backward stochastic differential equations and applications to optimal control, SIAM J. Control Optimization, Volume 37 (1999) no. 3, pp. 825-843 | DOI | MR | Zbl
[6] Eigenvalues of stochastic Hamiltonian systems driven by Poisson process with boundary conditions, Bound. Value Probl., Volume 2017 (2017), 164 | MR | Zbl
Cited by Sources:
Comments - Policy