Existence–uniqueness and continuation theorems for stochastic functional differential equations
By Daoyi Xu, Zhiguo Yang, Yumei Huang. 2008
58 citations recorded by the source corpus.
Abstract The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence–uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence–uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results.
Subfields: Applied Mathematics, Control and Systems Engineering, Finance
View Paper: https://www.semanticscholar.org/paper/1444ee8955ad7d44ee62dd9e00ea7703a41888ca
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In Applied Mathematics
In Control and Systems Engineering
In Finance
Citations in the corpus
- Backward stochastic differential equations with time delayed generators - results and counterexamples (2010, unknown): “See, for example, [11, 15] and references therein.”
- Existence and uniqueness of solutions of stochastic functional differential equations (2008, background): “Keywords: Stochastic functional differential equation, existence of solution, maximal solution, uniqueness of solution, Dereich lemma, stochastic Gronwall lemma.”