The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay

By Fengying Wei, Ke Wang. 2007

123 citations recorded by the source corpus.

Abstract This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC ( ( − ∞ , 0 ] ; R d ) . Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [ t 0 , T ] . Moreover, the existence-and-uniqueness theorem still holds on interval [ t 0 , ∞ ) , where t 0 ∈ R is an arbitrary real number.

Subfields: Computational Theory and Mathematics, Finance, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4112e0259c910d961fd180415cc372718a2e7829

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In Computational Theory and Mathematics

1. P. Revathi
2. Yong Ren
3. Rathinasamy Sakthivel
4. Q. Bi

In Finance

1. Rathinasamy Sakthivel
2. Yong Ren
3. Q. Bi
4. P. Revathi
5. Yuanguo Zhu
6. Zuomao Yan
7. Hongwu Zhang
8. K. Thiagu

In Numerical Analysis

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2. Yong Ren
3. Rathinasamy Sakthivel
4. Q. Bi
5. Yuanguo Zhu

Citations in the corpus

• Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay (2008, background): “Following this way, Wei and Wang [7] considered one such class of the so-called stochastic functional differential equations with infinite delay (ISFDEs in short) at phase space BC((−∞, 0]; R) to be described below.”
• Existence of solutions for nonlinear fractional stochastic differential equations (2013, background): “Wei and Wang [28] considered a class of stochastic functional differential equations with infinite delay in which the initial value belongs to the phase space.”
• Existence–uniqueness and continuation theorems for stochastic functional differential equations (2008, unknown): “Many important results can be found in [1–19] and references cited therein.”
• Stochastic functional differential equations with infinite delay driven by G‐Brownian motion (2013, methodology): “Wei F, Wang K.”