A note on the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay

作者：Ren Yong^*; Xia Ningmao

来源：Applied Mathematics and Computation, 2009, 214(2): 457-461.

DOI：10.1016/j.amc.2009.04.013

• Neutral stochastic functional differential equation
• Infinite delay
• Caratheodory-type condition

In this note, we prove the existence and uniqueness of the solution to neutral stochastic functional differential equations with infinite delay (INSFDEs in short) in which the initial value belongs to the phase space BC((- infinity, 0]R(d)), which denotes the family of bounded continuous R(d)-value functions phi defined on (-infinity,0] with norm parallel to phi parallel to = sup(-infinity<theta <= 0)vertical bar phi(theta)vertical bar, under some Caratheodory-type conditions on the coefficients by means of the successive approximation. Especially, we extend the results appeared in Ren et al. [Y. Ren, S. Lu, N. Xia, Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay, J. Comput. Appl. Math. 220 (2008) 364-372], Ren and Xia [Y. Ren, N. Xia, Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay, Appl. Math. Comput. 210 (2009) 7279] and Zhou and Xue [S. Zhou, M. Xue, The existence and uniqueness of the solutions for neutral stochastic functional differential equations with infinite delay, Math. Appl. 21 (2008) 75-83].

• 出版日期2009-8-15
• 单位华东理工大学