The improved LaSalle-type theorems for stochastic functional differential equations
The improved LaSalle-type theorems for stochastic functional differential equations
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DOI：
10.1016/j.jmaa.2005.05.026
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发表时间：
2006-06
影响因子：
1.3
通讯作者：
Yi Shen;Qi Luo;X. Mao
中科院分区：
文献类型：
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作者：
Yi Shen;Qi Luo;X. Mao
本文的主要目的是改进MAO[X.MAO，随机泛函微分方程的Lasalle型定理，非线性研究]的一些结果。7(2000)307-328]。当施加的条件比上述条件弱得多时，我们的新定理给出了更好的结果。例如，我们只需要解的局部Lipschitz条件，而不需要解的线性增长条件或有界矩条件。在较弱的条件下，为了保证基本随机泛函微分方程解的存在唯一性，我们建立了一个推广的存在唯一性定理，它涵盖了更广泛的一类非线性随机泛函微分方程解的存在唯一性，如本文所讨论的例子所示。此外，从我们改进的结果中得到了一些关于SFDE随机渐近稳定性的新的判据。
The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307–328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs.