|
|
G-Brown运动驱动的非线性随机泛函微分方程解的存在唯一性
|
Abstract:
目前，关于证明G-Brown运动驱动的非线性随机泛函微分方程解的全局存在唯一性的成果相对较少。本文利用G-Lyapunov函数方法获得了一类G-Brown运动驱动的非线性随机泛函微分方程解的全局存在唯一性的充分条件。最后，通过一个例子说明所得出的结论。
There are not so many results on the existence and uniqueness of solutions to nonlinear stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). By G-Lyapunov function technique, the existence and uniqueness of the global solution to a G-SFDE is obtained. Finally, an example is presented to illustrate the obtained theory.
| [1] | Mao, X. (1997) Stochastic Differential Equations and Application. Horwood Publishing, Chichester. |
| [2] | Arnold, L. (2007) Stochastic Differential Equations: Theory and Applications. World Scientific, Singapore. |
| [3] | Mohammed, S.E.A. (1984) Stochastic Functional Differential Equations. Pitman (Advanced Publishing Program), Boston, MA. |
| [4] | Mao, X. (1996) Razumikhin-Type Theorems on Exponential Stability of Stochastic Functional Differential Equations. Stochastic Processes and their Applications, 65, 233-250. https://doi.org/10.1016/S0304-4149(96)00109-3 |
| [5] | Hussein, A.K. (2020) Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay. Journal of Systems Science and Information, 8, 50-62.
https://doi.org/10.21078/JSSI-2020-434-13 |
| [6] | Shen, G., Xu, W. and Zhu, D. (2020) The Stability with General Decay Rate of Neutral Stochastic Functional Hybrid Differential Equations with Lévy Noise. Systems & Control Letters, 143, 104742.
https://doi.org/10.1016/j.sysconle.2020.104742 |
| [7] | Peng, S. (2007) G-Expectation, G-Brownian Motion and Related Stochastic Calculus of It？ Type. In: Benth, F.E., Di Nunno, G., Lindstr？m, T., ？ksendal, B. and Zhang, T., Eds., Stochastic Analysis and Applications. Abel Symposia, Vol. 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70847-6_25 |
| [8] | Peng, S. (2010) Nonlinear Expectations and Stochastic Calculus under Uncertainty. ArXiv:1002.4546. |
| [9] | Faizullah, F., Farkhanda, F. and Hussain, F. (2016) A Note on the Existence Results for Stochastic Functional Differential Equations Driven by G-Brownian Motion. Journal of Computational and Theoretical Nanoscience, 13, 8249-8253.
https://doi.org/10.1166/jctn.2016.5965 |
| [10] | Faizullah, F. (2017) Existence and Uniqueness of Solutions to SFDEs Driven by G-Brownian Motion with Non-Lipschitz Conditions. Journal of Computational Analysis and Applications, 23, 344-354. |
| [11] | Chen, Z. and Yang, D. (2020) Nonlocal Stochastic Functional Differential Equations Driven by G-Brownian Motion and Mean Random Dynamical Systems. Mathematical Methods in the Applied Sciences, 43, 7424-7441.
https://doi.org/10.1002/mma.6480 |
| [12] | Fei, C., Fei, W.Y. and Yan, L.T. (2019) Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion. Applied Mathematics: A Journal of Chinese Universities, 34, 184-204. https://doi.org/10.1007/s11766-019-3619-x |
